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#1 2009-01-09 13:31:50

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Finite sum of a power

How to calculate

If you already know the formulas for

for
, then you can calculate
using the following trick:

You expand the LHS and use the formulas you already know.

For example, the following formulas should be familiar to most people:

You can then apply the above trick to prove that

And with that, you can go on and find

. And so on, and so forth. smile


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#2 2009-01-09 14:15:24

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Finite sum of a power

Fanatstic result!

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#3 2009-01-09 18:43:10

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,164

Re: Finite sum of a power

That is both interesting and very useful!
Thanks for sharing this, JaneFairFax!
That it can be extended to any power makes it all the more interesting! smile


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