Prove the identity:

for .

*Proof.*For the case on the left we have,

While, on the right we have,

So, the identity holds in the case . Assume then that it holds for some . Then we have,

Hence, the statement is true for , and so, for all

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Stumbling Robot

A Fraction of a Dot
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Use an induction and properties of the product to prove an identity

* Proof. * For the case on the left we have,
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Prove the identity:

for .

While, on the right we have,

So, the identity holds in the case . Assume then that it holds for some . Then we have,

Hence, the statement is true for , and so, for all

This proof is wrong. When you multiply (1+ x^(2*m)).(1 – x^(2*m)) the result should be equals to (1-x^(4m))