What do you mean by "get from ... to ..."? The equality of these two expressions seems to hold only for k = 1: WolframAlpha.
Could you post the original problem?
sorry for the bad bracketing, this is the original question, im still massively confused by this.
Use mathematical induction to prove that
Σ 2/r(r^2-1) = (1/2) - (1/n(n+1)) n= 2,3,4.......
i have done the basic proof and got to the point
Σ = (1/2) - (1/k(k+1)) + 2/(k+1)(k+1^2-1)
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!