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Limit of a strange sequence

  • Thread starter JJ6
  • Start date
  • #1
JJ6
13
0

Homework Statement



I need to find the limit of the sequence:

[(1+1/n)(1+2/n)(1+3/n)...(1+n/n)]^(1/n) as n approaches infinity.

I know that the limit should come out to 4/e, but I cannot figure out why.

Homework Equations



None.

The Attempt at a Solution



The original sequence is equivalent to [(2n)!/(n!*n^n)]^(1/n), but I have absolutely no idea what to do with it after that. Can anybody point me in the right direction?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Why not just apply Stirling's approximation to the original sequence?
 

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