Infinite/Maclaurin Series problem!!

Evaluate the following: Riemann Sum k=2 to infinity, 2/(k^2 -1)

I'm not really sure where to begin...I rearranged the equation to -2/( 1 - k^2) and used the Maclaurin Series for 1/(1 - x) to obtain -2 * k^(2n). Interval of convergence for k is -1 < k < 1. Now I'm stuck as to how to evaluate it.

Re: Infinite/Maclaurin Series problem!!

Remember partial fractions:

$\displaystyle {2\over k^2-1}={1\over k-1}-{1\over k+1}$

Now see if you have a telescoping series. By the way this is a series __not__ a Riemann sum.

Re: Infinite/Maclaurin Series problem!!

Achiu 17

for k=2 till infinity Σ[2/(k^2 -1]=3/2 easy.