Hello. Need some help on solving this one:

Review the convergence of the following serie:

$\displaystyle 1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...+\frac {1}{n!}+...$

Thanks in advance.

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- Jan 9th 2011, 11:51 AMjavaxConvergence of a serie.
Hello. Need some help on solving this one:

Review the convergence of the following serie:

$\displaystyle 1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...+\frac {1}{n!}+...$

Thanks in advance. - Jan 9th 2011, 12:55 PMKrizalid
that's a known series, try ratio test.

- Jan 9th 2011, 01:48 PMjavax
Ok, thanks.

I knew it was convergent in the first place. By ratio test i see that it is convergent.

I've tested for n=50 and I see that it converges to number $\displaystyle e$, it approximates up to 14 digits. But can I come to number $\displaystyle e$ somehow analitycally? - Jan 9th 2011, 01:51 PMRandom Variable
It's the Maclaurin series for $\displaystyle e^{x} $ evaluated at $\displaystyle x= 1 $

- Jan 9th 2011, 01:53 PMPlato
$\displaystyle \displaystyle e^x = \sum\limits_{k = 0}^\infty {\frac{{x^k }}

{{k!}}} $