Reduction formula problem

Hi,

Here is the problem. The integral is defined by

where is a positive integer. Evaluate , and hence evaluate leaving your answer in the form of a sum.

I was hoping someone could tell me if I was on the right track or not. Firstly, is this an improper integral? If it is, how would I start the problem.

If it's not, I did the following

I fiddled about with this for a while and managed to get something but of course it's meaningless if the first part is wrong.

Any help would be much appreciated. :)

Thanks

Stonehambey