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# Use the following steps to prove $(17) .$ (a) Let $g(x)=\Sigma_{n=0}^{\infty}\left(\frac{k}{n}\right) x^{n} .$ Differentiate this series to show that $$g^{\prime}... ## Question ###### Use the following steps to prove (17) . (a) Let g(x)=\Sigma_{n=0}^{\infty}\left(\frac{k}{n}\right) x^{n} . Differentiate this series to show that$$g^{\prime}(x)=\frac{k g(x)}{1+x} \quad-1< x<1$$(b) Let h(x)=(1+x)^{-k} g(x) and show that h^{\prime}(x)=0 (c) Deduce that g(x)=(1+x)^{k}. Use the following steps to prove (17) . (a) Let g(x)=\Sigma_{n=0}^{\infty}\left(\frac{k}{n}\right) x^{n} . Differentiate this series to show that$$g^{\prime}(x)=\frac{k g(x)}{1+x} \quad-1< x<1 (b) Let $h(x)=(1+x)^{-k} g(x)$ and show that $h^{\prime}(x)=0$ (c) Deduce that $g(x)=(1+x)^{k}.$ #### Similar Solved Questions

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