Help with Telescopic Series with 3 terms in denominator 
All the examples i have done and seen only have 2 terms in the denominator so I am a bit stuck with this one. I have attached what I have done so far, not sure how to proceed with it.
Thank you for the hints they were useful, after working it out more I ended up with the following but now i am confused on what to do next, do I have to do another partial fraction decomposition?
My work after the hints

You are close to the end. Express what you got as
$$\left(\frac{1/2}{n}-\frac{1/2}{n+1}\right)-\left(\frac{1/2}{n+1}-\frac{1/2}{n+2}\right).$$
It looks a little better as
$$\frac{1/2}{n(n+1)}-\frac{1/2}{(n+1)(n+2)}.$$
Now add up, and (in either version) watch almost all the terms cancel.
