i have a power series of this form $\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^nx^n}{n} $ on attempting, i arrived at the sum-function $\displaystyle \frac{x}{n(1+x)} $ pls help if i missed it. thanks
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The result MUST NOT contain n, because n is the variable index for sumation. Derive the sum in order to get a geometric sum. After expressing the geometric sum as a closed form, integrate it.
Your sum is the same as $\displaystyle \sum_{n= 1}^\infty \frac{(-x)^n}{n}$. Do you know the Taylor series for ln(x+ 1) about x= 0?
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