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Question Number 31456 by rahul 19 last updated on 08/Mar/18

$$\mathbb{F}indsumof$$$$S=\frac{2}{3}+\frac{4}{3^2}+\frac{6}{3^3}+\frac{8}{3^4}+......+\mathrm{\infty }?$$

Commented by MJS last updated on 08/Mar/18

$$S_{\mathrm{\infty }}=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{2n}{k^n}=2\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{n}{k^n}=\frac{2k}{{(k-1)}^2}$$$$k=3\Rightarrow S_{\mathrm{\infty }}=\frac{3}{2}$$$$\mathrm{prove}\mathrm{is}\mathrm{somewhere}\mathrm{below}\mathrm{in}$$$$\mathrm{an}\mathrm{answer}\mathrm{to}\mathrm{a}\mathrm{former}\mathrm{question}$$

Commented by rahul 19 last updated on 09/Mar/18

$$thankusir!$$

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