Question

The sum $\sum _{k=1}^{\infty }\frac{2^{k+2}}{3^k}$ equal to

• A. 12
• B. 8
• C. 6
• D. 4

Answer 1

Answer: (B)

$S=4\sum _{k=1}^{\infty }{\left(\frac{2}{3}\right)}^k=4\left[\frac{2}{3}+{\left(\frac{2}{3}\right)}^2+{\left(\frac{2}{3}\right)}^3+\dots \dots ..\right]=4\left[\frac{2/3}{1-(2/3)}\right]=8$