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Differentiating and integrating power series Find the power series representation for $g$ centered at 0 by differentiating or integrating the power series for $f$ (perhaps more than once). Give the interval of convergence for the resulting series. $$g(x)=\frac{1}{(1-x)^{3}} \text { using } f(x)=\frac{1}{1-x}$$
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This function can be represented as a power series $\sum_{k=0}^{\infty} x^{k}$, which converges for $|x|<1$. Show more…
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