Does This Series Telesope and What is Its Partial Sum Formula?

[Firepanda]

I've been asked to show that the series:

http://img260.imageshack.us/img260/2676/asdaam0.jpg

That it telescopes, hence find a forumla for its partial sum, and then state the limit.

I'm sure I could find a formula for its partial sum IF I could simply show that it telescopes, for me I can't see how it does. Maybe I have a wrong definition of telescoping, but I thought it was when the majority of terms cancel, where in that series I can't see happening. Also I believe from inspection the limit is (ln 1).

Any help? :)

Thanks

 

[Avodyne]

It might help to notice that 1-1/k^2 = (k+1)(k-1)/k^2.

 

[Firepanda]

Yeah they gave us that as a hint. I can't see how it helps though :P

 

[HallsofIvy]

So
$$ln(1-\frac{2}{k^2})= ln(\frac{(k-1)(k+1)}{k^2}$$
What is THAT equal to?