Calculus Limits Problem (Homework)

Asked Aug 15 '20 at 07:42

Active Aug 15 '20 at 09:59

Viewed 82 times

$$\lim_{n\to \infty} \left[{\left({{n \choose 0}.{n \choose 1}.{n \choose 2}.\dots.{n \choose n}}\right)^\frac1{n^2+n}}\right]$$

I have tried to solve this question for a decent amount of time but with no avail,so I'd be grateful for any help provided.

ALSO:This may seem as a drag/nuisance, but are there any other alternate methods to solve this other than the one provided here?

edited Aug 15 '20 at 09:59

asked Aug 15 '20 at 07:42

Alan Whitteaker

7

can you show somethings that you have tried? also what calculus book is this from? page number and question number please. – jimjim Aug 15 '20 at 07:45
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Welcome to MSE. Why do you call it a sum? – José Carlos Santos Aug 15 '20 at 07:47
Maybe the answer is $ \infty $ ? – Spectre Aug 15 '20 at 08:10
@jimjim I don't have a source for this question,it was listed as one of the questions in the homework assignment. – Alan Whitteaker Aug 15 '20 at 08:12
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@Spectre I do not know the answer to the question so I wanted to know if this(answer being infinity) could be disproved. – Alan Whitteaker Aug 15 '20 at 08:14
Sorry, bro.... it was just a guess... – Spectre Aug 15 '20 at 08:15
@Marktmeister I had tried your approach earlier as well,but then you end up with the answer as infinity.I'm not entirely sure of this answer as I had seen somewhere this answer being solved by double summation. – Alan Whitteaker Aug 15 '20 at 08:33

0 Answers0