Use the derivative of the Taylor series about 0 for $\frac{1}{1-x}$ to find the Taylor series about 0 for $\frac{x}{(1-x)^{2}}$ .Use this result to find the value of $\frac{1}{4}+\frac{2}{16}+\frac{3}{64}+\frac{4}{256}+\frac{5}{1024}+\cdots$ .Round to 3 decimal places.

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The Answer of Use the derivative of the Taylor series about 0 for $\frac{1}{1-x}$ to find the Taylor series about 0 for $\frac{x}{(1-x)^{2}}$ .Use this result to find the value of $\frac{1}{4}+\frac{2}{16}+\frac{3}{64}+\frac{4}{256}+\frac{5}{1024}+\cdots$ .Round to 3 decimal places.

Use the Derivative of the Taylor Series About 0 For \frac{1}{1-x}