How to Find the Sum of 2^n/n! for n=2 to Infinity

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I need to find the sum of 2^n/n! from n=2 to infinity, i know that it converges to e^x but how do i find the sum?
 
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kj13529 said:
I need to find the sum of 2^n/n! from n=2 to infinity, i know that it converges to e^x but how do i find the sum?

It is e^2.
Since x^n/n! sums to e^x substitute x=2 to get answer.
 
Thanks, it was so simple -.-
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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