Prove the following limit below…(JEE PRACTICE TEST QUESTION) [closed]
1
$begingroup$
How do we prove the following limit below?
(Without Stirlings approximation)-$$lim_{nto infty}prod_{k=0}^n binom{n}{k}^{large {1over n(n+1)}} =e^{1/2}$$
calculus limits
asked Dec 21 '18 at 7:57
ReevReev
62
$endgroup$
closed as off-topic by Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad Dec 21 '18 at 8:26
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." – Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
1
$begingroup$
How do we prove the following limit below?
(Without Stirlings approximation)-$$lim_{nto infty}prod_{k=0}^n binom{n}{k}^{large {1over n(n+1)}} =e^{1/2}$$
calculus limits
asked Dec 21 '18 at 7:57
ReevReev
62
$endgroup$
closed as off-topic by Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad Dec 21 '18 at 8:26
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." – Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
$log$ both sides, use Stirling's, etc
$endgroup$
– mathworker21
Dec 21 '18 at 8:02
$begingroup$
Take logs and see this math.stackexchange.com/q/2809649/72031
$endgroup$
– Paramanand Singh
Dec 21 '18 at 14:37
add a comment |
1
1
1
$begingroup$
How do we prove the following limit below?
(Without Stirlings approximation)-$$lim_{nto infty}prod_{k=0}^n binom{n}{k}^{large {1over n(n+1)}} =e^{1/2}$$
calculus limits
asked Dec 21 '18 at 7:57
ReevReev
62
$endgroup$
How do we prove the following limit below?
(Without Stirlings approximation)-$$lim_{nto infty}prod_{k=0}^n binom{n}{k}^{large {1over n(n+1)}} =e^{1/2}$$
calculus limits
calculus limits
asked Dec 21 '18 at 7:57
ReevReev
62
asked Dec 21 '18 at 7:57
ReevReev
62
edited Dec 21 '18 at 12:07
Reev
asked Dec 21 '18 at 7:57
ReevReev
62
asked Dec 21 '18 at 7:57
ReevReev
62
asked Dec 21 '18 at 7:57
ReevReev
62
62
closed as off-topic by Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad Dec 21 '18 at 8:26
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." – Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad Dec 21 '18 at 8:26
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." – Arnaud D., Claude Leibovici, Martin R, Chinnapparaj R, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
$log$ both sides, use Stirling's, etc
$endgroup$
– mathworker21
Dec 21 '18 at 8:02
$begingroup$
Take logs and see this math.stackexchange.com/q/2809649/72031
$endgroup$
– Paramanand Singh
Dec 21 '18 at 14:37
add a comment |
1
$begingroup$
$log$ both sides, use Stirling's, etc
$endgroup$
– mathworker21
Dec 21 '18 at 8:02
$begingroup$
Take logs and see this math.stackexchange.com/q/2809649/72031
$endgroup$
– Paramanand Singh
Dec 21 '18 at 14:37
1
1
$begingroup$
$log$ both sides, use Stirling's, etc
$endgroup$
– mathworker21
Dec 21 '18 at 8:02
$begingroup$
$log$ both sides, use Stirling's, etc
$endgroup$
– mathworker21
Dec 21 '18 at 8:02
$begingroup$
Take logs and see this math.stackexchange.com/q/2809649/72031
$endgroup$
– Paramanand Singh
Dec 21 '18 at 14:37
$begingroup$
Take logs and see this math.stackexchange.com/q/2809649/72031
$endgroup$
– Paramanand Singh
Dec 21 '18 at 14:37
add a comment |
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1
$begingroup$
$log$ both sides, use Stirling's, etc
$endgroup$
– mathworker21
Dec 21 '18 at 8:02
$begingroup$
Take logs and see this math.stackexchange.com/q/2809649/72031
$endgroup$
– Paramanand Singh
Dec 21 '18 at 14:37