Hello,

I need to:

Determine if series is convergent or divergent. If convergent, Find its sum.

I have a problem: Summation from n=2 to infinity of: 2/(n^2 - 1)

The limit as n-> infinity of 2/(n^2 - 1) is 0, so the divergence test fails.

I think what i'm left to work with is whether it's a harmonic, telescoping, or geometric series.

If I drop the index of the summation from n=2 to n=1, 2/(n^2 - 1) becomes 2/[(n + 1)^2 - 1] I believe... Then if I evaluate it:

a1 = 2/3

a2 = 2/3 + 1/4

a3 = 2/3 + 1/4 + 2/15

a4 = 2/3 + 1/4 + 2/15 + 1/12

Is this correct? I'm not sure how to tell if this is convergent/divergent from this. I don't recognize this as a harmonic, telescoping, or geometric sequence... any ideas?

## Bookmarks