Question

How i calculate the value of the sum `2^(n+3)/(n!)` ?

Answer 1

`2^3e^2`

Explanation:

`e^x = sum_{i=0}^{oo}x^i/(i!)`

so

`e^2 = sum_{i=0}^{oo}2^i/(i!)`

then

`2^3sum_{i=0}^{oo}2^i/(i!) = sum_{i=0}^{oo}2^{i+3}/(i!) = 2^3e^2`