Use mathematical induction to prove that

n

Σ 2/r(r^2-1) = (1/2) - (1/n(n+1)) n= 2,3,4.......

r=2

i have done the basic proof and got to the point

k+1

Σ = (1/2) - (1/k(k+1)) + 2/(k+1)(k+1^2-1)

r=2

I think i need to get to (1/2) - 1/(k+1)(k+2) but im not sure how to get there, any help would be greatly appreciated!