# Series converge/ diverges. determine sum of series

## Main Question or Discussion Point

Determine if the series converges or diverges ad if it converges then determine the sum of the series analytically:

infinity
{Sigma} 2/n(n+2)
n=1

so i used partial fractions and got:
{Sigma} [1/n + 1/(n+2)]

then i used telescoping form to get the nth partial sum...
Sn= (1/1 + 1/3) + (1/2 + 1/4) +...

then i got the nth partial sum to be = 1+1/(n+2)

so the series converges and its sum is 1?

Does that seem right to everyone?

Char. Limit
Gold Member
First, this is in the wrong section, I believe. It should go in the homework and coursework area.

Second, yes. However, be careful...

As you did the work wrong, and yet got the right answer. The partial fraction decomposition for $\frac{2}{(n)(n+2)}$ isn't quite what you posted. Can you see the error?

oh ok. i thought this was the homework and course area.

yea its supposed to be subtraction, not addition. i got 3/2 to be the sum of the series

Char. Limit
Gold Member
There you go.

You win...