Hi, Aidan!
If you are interested in summation look at http://en.wikipedia.org/wiki/User:Ascoldcaves. The full proof of the summation formula you can see at www.oddmaths.info/indefinitesum. In the article there is a single summation formula to sum any analytical function with any summation boundaries. If you are a user of “Mathematica” there is at the bottom left of the page of the site a button “examples”. Opening the examples in “Mathematica” you can choose an analytical function at your choice and arbitrary complex boundaries and calculate your sum.
By,
Ascold.
Ascoldcaves (talk) 20:44, 4 March 2012 (UTC)