need help figuring out what R is for the following power series...
summation from 0 to infinity {[(1+5^n)/n!]x^n]}
I suggested:
$\displaystyle e^x+e^{5\cdot{x}}=\sum_{n=0}^{\infty}{\left(\frac{ 1+5^n}{n!}\right)}\cdot{x^n}$ for all real $\displaystyle x$ which is the series you wanted
I do not see sin (n) there
But if you want to do it by the root test you just have to remember that $\displaystyle \lim_{n\rightarrow{+\infty}}\frac{\sqrt[n]{n!}}{\frac{n}{e}}=1$