Find $\sum _0^{\infty} \frac{1}{2^nn!}$

Question

Find $$\sum_{n=0}^{\infty} \frac{1}{2^nn!}$$

I know it's less than $$2 = \sum_{n=0}^{\infty} \frac{1}{2^n}$$

$\sqrt{\sum_{k=0}^{\infty}{\frac{1}{k!}}} = \sqrt{e}$ – Tacet Nov 19 '14 at 00:55 — Tacet, Nov 19 '14 at 00:55

score 15 · Answer 1 · answered Nov 19 '14 at 00:50

15

Hint: $$e^{x} = \sum_{n=0}^{\infty} \frac{x^{n}}{n!}$$

answered Nov 19 '14 at 00:50

Alex Wertheim

1 Answers1