(See Solution) Prove that the series 1+2x+x^2+2x^3+x^4+2x^5+.... is equal to
Question: Prove that the series
\[1+2x+{{x}^{2}}+2{{x}^{3}}+{{x}^{4}}+2{{x}^{5}}+....\]is equal to \(\frac{2x+1}{1-{{x}^{2}}}\).
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