Math Is Fun Forum

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.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Finite sum of a power

Fanatstic result!

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,406

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!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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