Closed form of a partial sum?

Hey fellow math people,

I'm Matt, new to the board and looking forward to reading posts and learning as much as I can so I can get through my calc II class and beyond.

To start, I'm having trouble with finding the closed form of an *n*th partial sum of an infinite series. Here's the question given:

ln(1/2) + ln(2/3) + ln(3/4) +...+ ln(k/k+1) +...

Directions say to find closed form and if it converges, find limit.

Any help appreciated, I'm having trouble comprehending the process of finding a closed form. I know you subtract (Sn) from some other form of the series--but what's the common ratio betwee the two? Or am I going off on a tangent...

Thanks!

Matt