This series of positive terms is absolutely convergent, as shown by the Ratio test, based on the following calculation.

$L\=\underset{n\to \infty }{lim}\left|\frac{a_{n\+1}}{a_n}\right|$ = $\underset{n\to \infty }{lim}\frac{{10}^{n\+1}\/\left(n\+1\right)\!}{{10}^n\/n\!}$ = $\underset{n\to \infty }{lim}\frac{10}{n\+1}\=0$ 

Since $L$ is less than 1, the series converges absolutely.

Showing that this series of positive terms has the explicit sum $e^{10}$ would actually establish its absolute convergence, provided that Maple's internal manipulations were exposed. Short of that, either the details of the summation would need to be provided, or the Ratio test implemented.