Re: Mathematical Induction

Quote:

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

$\displaystyle \frac{1}{2}-\frac{1}{k(k+1)}+\frac{2}{(k+1)((k+1)^2-1)}=~?$

Re: Mathematical Induction

Re: Mathematical Induction

Quote:

Originally Posted by

**gurnster76** That's where im stuck.

$\displaystyle \frac{2}{(k+1)((k+1)^2-1)}=\frac{2}{(k+1)(k^2+2k)}=\frac{2}{k(k+1)(k+2)}$

Re: Mathematical Induction

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)