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User:Ans/Sum of Sequence of Squares

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Theorem

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{{:proofwiki:Sum of Sequence of Squares/Proof by Induction}}

{{:proofwiki:Sum of Sequence of Squares/Proof by Products of Consecutive Integers}}

{{:proofwiki:Sum of Sequence of Squares/Proof by Telescoping Series}}

Proof by Summation of Summations

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File:Sum of Sequences of Squares.jpg

We can observe from the above diagram that:

Therefore we have:

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Proof by Sum of Differences of Cubes

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On the other hand:

Therefore:

Therefore:

Template:Qed

{{:proofwiki:Sum of Sequence of Squares/Proof by Binomial Coefficients}}

{{:proofwiki:Sum of Sequence of Squares/Proof using Bernoulli Numbers}}

{{:proofwiki:Sum of Sequence of Squares/Historical Note}}

Sources

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