I need some hint to find the sum of the series. $$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n3^n}$$ I calculated using mathematica. it gives the sum as $\log(3/2)$
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Use the expansion
$$-\log{(1-x)} = \sum_{n=1}^{\infty} \frac{x^n}{n} $$
Then you should get
$$-\log{\frac{2}{3}} = \log{3}-\log{2} = \sum_{n=1}^{\infty} \frac1{n 3^n}$$
Ron Gordon
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Are there any other way to find the sum without using power series expansion? – Raio May 13 '14 at 10:54
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3Well, you could take a derivative to obtain a geometrical sum, then integrate. – Ron Gordon May 13 '14 at 10:55