Making use of the method of differences, prove that

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- Sep 6th 2011, 05:12 AMPunchMethod of difference (proving)
Making use of the method of differences, prove that

- Sep 15th 2011, 08:59 PMCaptainBlackRe: Method of difference (proving)
If you write out the first few terms you will find that the only terms at the begining of the summation that do not cancel out are:

similarly if you look at the middle of the summation you will see that all terms cancel and at the end the terms that do not cancel are:

Alternatively for k even you can turn this into a more obviously telescoping series by combining terms in pairs.

CB