Question

Find the value of ${\sum }_{i=0}^{\infty }$ $\frac{1}{5}\frac{1}{3^i}$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

${\sum }_{i=0}^{\infty }$ $\frac{1}{5}\frac{1}{3^i}$.

Bring constant term outside the summation part and then proceed.

$\frac{1}{5}$ ${\sum }_{i=0}^{\infty }$ $\frac{1}{3^i}$.

= $\frac{1}{5}$ $[\frac{1}{3^0}+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+.....\infty ]$

= $\frac{1}{5}$ $[1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+.....\infty ]$

= $\frac{1}{5}$ $\left(\frac{1}{1-\frac{1}{3}}\right)$ = $\frac{1}{5}$ $\times$ $\frac{3}{2}$ = $\frac{3}{10}$