Find-sum-of-S-2-3-4-3-2-6-3-3-8-3-4-

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

F i n d s u m o f

S = \frac{2}{3} + \frac{4}{3^{2}} + \frac{6}{3^{3}} + \frac{8}{3^{4}} + \dots \dots + \infty ?

Commented by MJS last updated on 08/Mar/18

S_{\infty} = \underset{n = 1}{\sum^{\infty}} \frac{2 n}{k^{n}} = 2 \underset{n = 1}{\sum^{\infty}} \frac{n}{k^{n}} = \frac{2 k}{{(k - 1)}^{2}}

k = 3 \Rightarrow S_{\infty} = \frac{3}{2}

prove is somewhere below in

an answer to a former question

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

t h a n k u s i r!