\sum^{\infty}_{k=0} 2^k/3^{k+1}

TS ICET 2015 Question Paper with Solutions for online practice

Question : 135 of 200

Marks: +1, -0

Σ↖{∞}↙{k=0}

2^k/3^{k+1}

Solution:

∑↙{k=0}↖{∞}{2^{k}}/{3^{k+1}}={1}/{3}+{2}/{3^{2}}+{2^{2}}/{3^{3}}+{2^{3}}/{3^{4}}+. . .

It is an infinite G.P.;

a=1/3,r=2/3 < 1

∴S=a/{1-r}={1{/}3}/{(1-2/3)}=1

Go to Question:

Prev Question

Next Question