i tried... i can't get tackle with this problem no matter how hard i try. please help me.

http://i1182.photobucket.com/albums/...irasi/2624.jpg

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- Dec 4th 2011, 01:42 AMmamia problem about series
i tried... i can't get tackle with this problem no matter how hard i try. please help me.

http://i1182.photobucket.com/albums/...irasi/2624.jpg - Dec 4th 2011, 08:14 AMOpalgRe: a problem about series
It looks to me very much as though this series diverges. In fact, a bit of work with a pocket calculator suggests that $\displaystyle e - \bigl(1+\tfrac1n\bigr)^n > \tfrac1n$ whenever $\displaystyle n\geqslant3.$ More precisely, I'm finding that $\displaystyle n\Bigl(e - \bigl(1+\tfrac1n\bigr)^n\Bigr)$ converges to a limit approximately 1.36 as $\displaystyle n\to\infty.$

- Dec 4th 2011, 08:16 AMgirdavRe: a problem about series
The series has non-negative terms, and $\displaystyle e-\left(1+\frac 1n\right)^n\sim\frac e{2n}$ hence the series diverges, hence the sum is $\displaystyle +\infty$.