# How do you use a power series to find the exact value of the sum of the series 1+2+4/(2!) +8/(3!) +16/(4!) + … ?

1+x+x^2/{2!}+x^3/{3!}+x^4/{4!}+cdots=e^x,
by replacing $x$ by $2$,
1+2+2^2/{2!}+2^3/{3!}+2^4/{4!}+cdots=e^2.