# Thread: series convergence and sum

1. ## series convergence and sum

I know this series converges by graphing it, but im confused on how to go about solving it and computing the sum.

the sum from n=2 to INF of 2/((4n^2) - 1)

2. $2=(2n+1)-(2n-1).$

It's a telescoping series.

3. Im still kind of lost, im taking this class through the mail, so i do not have a teacher to help out at all. Im trying to study for the final and i struggled through sequences and series.

4. Originally Posted by mikemurphy
Im still kind of lost, im taking this class through the mail, so i do not have a teacher to help out at all. Im trying to study for the final and i struggled through sequences and series.
a telescopic series is one which has (for example) sum of two terms in n-th place, both of which cancel with one term from (n-1)th and (n+1)th each respectively. finally you can just see what is the sum ... try it ... it is straightforward.