I'm trying to find the sum of this infinite series (with n=2) of

6/(n^2-1)

for some reason my answer isn't matching up with the answer choices.

What I did:

1/(n+1)-1/(n-1)

Sn=(1/3-1)+(1/4-1/2)+(1/5 - 1/3)+.....+(1/(n-1)-1/(n-3))+(1/n - 1/(n-2))+(1/(n+1)- 1/(n-1))

after canceling things out and taking the limit I ended up with -1-(1/2)=-3/2

Can somebody please tell me what I'm doing wrong. Any help is appreciated, thank you!