Find the sum of the series.

[njmiano]

I am asked to find if this series converges or diverges, if it converges I am to find the sum.
I have no problem finding that it converges, however I am having problems finding the sum. (I am having problems finding sums of infinite series in general, unless it is a perfect looking geometric series, so any expanded help on finding sums, or a link to good online lessons about the subject would be appreciated.)

(Sum of the series, n = 1 to infinity) [( 1 / e^n) + (1 / n(n+1)]

I know from earlier problems that the sum of 1 / n(n+1) = 1, and I believe I would set up the other part as
(1/e * [(1/e) / (1 - (1/e))])
please help.

 

[pka]

Because these are absolutely convergent rearrange them.
\(\displaystyle \sum\limits_{n = 1}^\infty {\left[ {\frac{1}{{e^n }} + \frac{1}{{n\left( {n + 1} \right)}}} \right]} = \sum\limits_{n = 1}^\infty {\left[ {\frac{1}{{e^n }}} \right]} + \sum\limits_{n = 1}^\infty {\left[ {\frac{1}{n} - \frac{1}{{n + 1}}} \right]} = \frac{{\frac{1}{e}}}{{1 - \frac{1}{e}}} + 1\)