Question: Prove the geometric series formula Use this to explain why P is really 1 1-2 = 1+x+x + k=0 ak k X

Prove the geometric series formula

( frac{1}{1-x}=1+x+x^{2}+cdots=sum_{k=0}^{infty} x^{k} )

Use this to explain why P is really

( P=left[left(1+frac{1}{2^{2}}+frac{1}{2^{4}}+cdotsight)left(1+frac{1}{3^{2}}+frac{1}{3^{4}}+cdotsight)left(1+

1 1-2 = 1+x+x + k=0 ak k X

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