# Calculus: computation of $\sum \frac{2^i}{i!}$

$$\sum_{i=0}^\infty \frac{2^i}{i!}$$

Would anyone mind telling me what is the answer? I know this may be a silly question but I would like to know.

• What is the power series representation of $e^x$? – David Mitra Nov 23 '13 at 13:20

The Maclaurin expansion of $e^x$ is: $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$
So therefore: $$\sum_{i=0}^\infty \frac{2^i}{i!} = e^2 \approx 7.389$$