Some help with the following would be appreciated!

Find (and prove) a formula for Σ from j=1 to k of j^3

Known propositions:

Σ from j=1 to k of j = k(k+1) / 2

Σ from j=1 to k of j^2 = k(k+1)(2k+1) / 6

Thank you!

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- Feb 25th 2011, 03:23 PMjstarks44444Summation formula
Some help with the following would be appreciated!

Find (and prove) a formula for Σ from j=1 to k of j^3

Known propositions:

Σ from j=1 to k of j = k(k+1) / 2

Σ from j=1 to k of j^2 = k(k+1)(2k+1) / 6

Thank you! - Feb 25th 2011, 05:16 PMBruno J.
Note that

.

Hence

.

Now use what you know! - Feb 25th 2011, 07:44 PMSoroban
Helolo, jstarks44444!

Quote:

. .

We note that: .

Let

And we have this "stack" of equations:

. .

Add the entire stack of equations and we have:

. .

Substitute the known formulas:

. .

. .

Then we have:

. .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

- Feb 25th 2011, 10:19 PMchisigma