Trouble with a limit of an infinite product [on hold]
2
I am having problems with this product. I've never really encountered problems like this, so if anyone has some good reads on these kinds of problems, please let me know.
$$lim_{ntoinfty}prod_{k=1}^{n}frac{k^2+k-1}{k(k+1)}$$
Thanks in advance ^^
calculus limits infinite-product
edited yesterday
Rebellos
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asked yesterday
Boxonix
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put on hold as off-topic by mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
2
I am having problems with this product. I've never really encountered problems like this, so if anyone has some good reads on these kinds of problems, please let me know.
$$lim_{ntoinfty}prod_{k=1}^{n}frac{k^2+k-1}{k(k+1)}$$
Thanks in advance ^^
calculus limits infinite-product
edited yesterday
Rebellos
14.3k31245
asked yesterday
Boxonix
194
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers
If this question can be reworded to fit the rules in the help center, please edit the question.
If the factors are positive (as they are here), then a boilerplate tactic is to take logarithms, thereby turning the "infinite" product into a series. But first it often pays to look for special properties of the factors that simplify your consideration. It isn't clear whether you are looking for "good reads on these kinds of problems" or help with this specific infinite product. Please add more context.
– hardmath
yesterday
add a comment |
2
2
2
2
I am having problems with this product. I've never really encountered problems like this, so if anyone has some good reads on these kinds of problems, please let me know.
$$lim_{ntoinfty}prod_{k=1}^{n}frac{k^2+k-1}{k(k+1)}$$
Thanks in advance ^^
calculus limits infinite-product
edited yesterday
Rebellos
14.3k31245
asked yesterday
Boxonix
194
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I am having problems with this product. I've never really encountered problems like this, so if anyone has some good reads on these kinds of problems, please let me know.
$$lim_{ntoinfty}prod_{k=1}^{n}frac{k^2+k-1}{k(k+1)}$$
Thanks in advance ^^
calculus limits infinite-product
calculus limits infinite-product
edited yesterday
Rebellos
14.3k31245
asked yesterday
Boxonix
194
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Rebellos
14.3k31245
asked yesterday
Boxonix
194
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Rebellos
14.3k31245
edited yesterday
Rebellos
14.3k31245
edited yesterday
Rebellos
14.3k31245
14.3k31245
asked yesterday
Boxonix
194
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Boxonix
194
asked yesterday
Boxonix
194
194
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Boxonix is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, amWhy, José Carlos Santos, Paul Frost, Brian Borchers
If this question can be reworded to fit the rules in the help center, please edit the question.
If the factors are positive (as they are here), then a boilerplate tactic is to take logarithms, thereby turning the "infinite" product into a series. But first it often pays to look for special properties of the factors that simplify your consideration. It isn't clear whether you are looking for "good reads on these kinds of problems" or help with this specific infinite product. Please add more context.
– hardmath
yesterday
add a comment |
If the factors are positive (as they are here), then a boilerplate tactic is to take logarithms, thereby turning the "infinite" product into a series. But first it often pays to look for special properties of the factors that simplify your consideration. It isn't clear whether you are looking for "good reads on these kinds of problems" or help with this specific infinite product. Please add more context.
– hardmath
yesterday
If the factors are positive (as they are here), then a boilerplate tactic is to take logarithms, thereby turning the "infinite" product into a series. But first it often pays to look for special properties of the factors that simplify your consideration. It isn't clear whether you are looking for "good reads on these kinds of problems" or help with this specific infinite product. Please add more context.
– hardmath
yesterday
If the factors are positive (as they are here), then a boilerplate tactic is to take logarithms, thereby turning the "infinite" product into a series. But first it often pays to look for special properties of the factors that simplify your consideration. It isn't clear whether you are looking for "good reads on these kinds of problems" or help with this specific infinite product. Please add more context.
– hardmath
yesterday
add a comment |
1 Answer
1
active
oldest
votes
1
Hint :
Note that :
$$k^2 + k -1 = k(k+1)-1$$
Thus the given expression is transformed to :
$$lim_{nto infty} prod_{k=1}^n frac{k(k+1)-1}{k(k+1)} = lim_{nto infty} prod_{k=1}^n left( 1 - frac{1}{k(k+1)}right)$$
answered yesterday
Rebellos
14.3k31245
1
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
2
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
1
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
|
show 6 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
Hint :
Note that :
$$k^2 + k -1 = k(k+1)-1$$
Thus the given expression is transformed to :
$$lim_{nto infty} prod_{k=1}^n frac{k(k+1)-1}{k(k+1)} = lim_{nto infty} prod_{k=1}^n left( 1 - frac{1}{k(k+1)}right)$$
answered yesterday
Rebellos
14.3k31245
1
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
2
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
1
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
|
show 6 more comments
1
Hint :
Note that :
$$k^2 + k -1 = k(k+1)-1$$
Thus the given expression is transformed to :
$$lim_{nto infty} prod_{k=1}^n frac{k(k+1)-1}{k(k+1)} = lim_{nto infty} prod_{k=1}^n left( 1 - frac{1}{k(k+1)}right)$$
answered yesterday
Rebellos
14.3k31245
1
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
2
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
1
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
|
show 6 more comments
1
1
1
Hint :
Note that :
$$k^2 + k -1 = k(k+1)-1$$
Thus the given expression is transformed to :
$$lim_{nto infty} prod_{k=1}^n frac{k(k+1)-1}{k(k+1)} = lim_{nto infty} prod_{k=1}^n left( 1 - frac{1}{k(k+1)}right)$$
answered yesterday
Rebellos
14.3k31245
Hint :
Note that :
$$k^2 + k -1 = k(k+1)-1$$
Thus the given expression is transformed to :
$$lim_{nto infty} prod_{k=1}^n frac{k(k+1)-1}{k(k+1)} = lim_{nto infty} prod_{k=1}^n left( 1 - frac{1}{k(k+1)}right)$$
answered yesterday
Rebellos
14.3k31245
answered yesterday
Rebellos
14.3k31245
answered yesterday
Rebellos
14.3k31245
answered yesterday
Rebellos
14.3k31245
14.3k31245
1
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
2
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
1
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
|
show 6 more comments
1
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
2
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
1
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
1
1
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
I'm sorry but this means nothing to me, as I've said i know nothing about these products. In fact, I've come this far on my own.
– Boxonix
yesterday
2
2
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
@Boxonix That's the intuitive step here. If you really know nothing, how come you are working over one ? Maybe you need some studying in general to get a handle of them.
– Rebellos
yesterday
1
1
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
This is a problem that has appeared last year on the test I'm taking tomorrow, the only knowledge we have are sequence limits, we haven't worked over any formulas regarding infinite series and products.
– Boxonix
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
@Boxonix I just saw you edited your comment mentioning that you've come this far, which was not mentioned before and not included in the question form (why?). Nevertheless, if that's a question that makes no sense to you and you haven't studied anything like that in your class, then maybe this part could have been removed from this years lessons. Also, exam on the 26th of December ?
– Rebellos
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
I'm from Bosnia, 26th is a work day. Being from Bosnia also means that assistants can do whatever they desire without it being regulated. Questions that assistants themselves can't answer are a common occurrence on the exams. I haven't posted that I've come this far because it was one of many manipulations I've tried, and I've thought it wouldn't lead me anywhere.
– Boxonix
yesterday
|
show 6 more comments
If the factors are positive (as they are here), then a boilerplate tactic is to take logarithms, thereby turning the "infinite" product into a series. But first it often pays to look for special properties of the factors that simplify your consideration. It isn't clear whether you are looking for "good reads on these kinds of problems" or help with this specific infinite product. Please add more context.
– hardmath
yesterday