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Question Number 130886 by Khalmohmmad last updated on 30/Jan/21

$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1+2^n}{3^n}$$

Answered by EDWIN88 last updated on 30/Jan/21

$$\underset{n=1}{\sum ^{\mathrm{\infty }}}{\left(\frac{1}{3}\right)}^n+\underset{n=1}{\sum ^{\mathrm{\infty }}}{\left(\frac{2}{3}\right)}^n=\frac{\frac{1}{3}}{1-\frac{1}{3}}+\frac{\frac{2}{3}}{1-\frac{2}{3}}$$$$=\frac{1}{2}+\frac{2}{1}=\frac{5}{2}$$

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