Yes, I presume you have a finite sum.Originally Posted byOReilly

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The key in the the fact that,

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Therefore, that entire sum is,

Thus,

Thus, subdivide the summation,

Use the fact above, and the sum of squares formula,

Simplify,

Add, common denominator and add,

Thus, (factor),

Simplify again,

Simplify again,

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Just for refernce, the sum of squares formula is,

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I think it is cool that,

That means you can calculate the sum by taking 2 more than number of terms and finding the number of combinations of forming three.