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 June 2nd, 2017, 12:32 AM #1 Senior Member   Joined: Nov 2015 From: hyderabad Posts: 206 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) $\displaystyle ( \frac{2n+1}{2n-2})^n$ 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: 17,919 Thanks: 1386 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: 6,307 Thanks: 526 Sequence C converges to e.
 June 17th, 2017, 04:19 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,653 Thanks: 681 "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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