Question

Find the sum of the series. Series from 0 to infinity 5En%7D" id="TexFormula1" title="\frac{7^n}{n!3^n}" alt="\frac{7^n}{n!3^n}" align="absmiddle" class="latex-formula">

Answer 1

Recall that

$e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}$

Plug in $x=\frac73$ and you get your series, so the given series has a value of $e^{7/3}$.