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June 2nd, 2017, 12:32 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 232 Thanks: 2  Which of the following series converges to e
Which of the following series converges to $e$ A) $\displaystyle (1+ \frac{1}{2n})^n $ B) $\displaystyle (2+ \frac{1}{2!}+\frac{1}{3!}+...+\frac{1}{n!}) $ C) $\displaystyle (1+ \frac{1}{n})^n $ D) $\displaystyle ( \frac{2n+1}{2n2})^n $ My answers are options A and C. Please correct me if I'm wrong Thank you 
June 2nd, 2017, 01:20 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,967 Thanks: 1607 
What does (B) converge to? The other choices aren't series, so what did you do when considering them?

June 3rd, 2017, 06:14 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,512 Thanks: 585 
Sequence C converges to e.

June 17th, 2017, 04:19 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,171 Thanks: 869 
"Sequence" is the right word, not "series". In (A), if we let i= 2n then n= i/2 so $\displaystyle \left(1+ \frac{1}{2n}\right)^n$ becomes $\displaystyle \left(1+ \frac{1}{i}\right)^{i/2}= \left[\left(1+ \frac{1}{i}\right)^i\right]^{1/2}$. Last edited by skipjack; June 17th, 2017 at 05:11 AM. 

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