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 for the reply
1) How does the fact that it's an improper integral change the result? (I did all the above working before I noticed this, d'oh!)
2) What is the question hinting at when it asks to be written in the form of a sum?
The question was lifted from the 1998 STEP II paper (Cambridge entrance exams) and since Fourier series are not on the A-level syllabus I don't think you need to use them in your answer, even if the problem is related to them (This is not uncommon).
Thanks for the help
Oh, I think I got it! I just forgot that what I (we) calculated is , and not itself, so we got a recursive formula:
, so we can try:
. (** Odd n. For even n take the preceeding value of n)
And now add both columns above:
. (Read ** above)