`sum` (2^n)/n!

Hello!

I assume the sum is from `n=0` to infinity. This series is (absolutely) convergent, which is simple to check by the Ratio test.

Consider the exponential function `e^x.` Its Taylor series is `sum_(n=0)^oo x^n/(n!),` and `e^x` is equal to the sum of this series for all real (and complex) `x.` The sum in question is therefore `e^2,` which is approximately `7.39.`