Question

The sum to infinity of the series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{10}{3^4}+....$ is

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is B 3

Let $S=1+2/3+6/3^2+\dots$

$S/3=1/3+2/3^2+6/3^3+\dots$

$S-S/3=1+1/3+4/3^2+4/3^3+\dots$

$2S/3=4/3+\frac{4/3^2}{1-1/3}$

$2S/3=4/3+2/3\Rightarrow S=3$

The correct option is B.