Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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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.

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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
Registered: 2005-06-28
Posts: 26,453

### 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!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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