Thread: Mathematical Induction

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!

Originally Posted by gurnster76

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

Work with

That's where im stuck.

Originally Posted by gurnster76

That's where im stuck.

but how do i get from

(1/2) - (1/k(k+1)) + (2/(k+1)(k+2)

to (1/2) - (1/(k+1)(k+2)