Question

The sum of the series $2\left[7^{-1}+3^1{.7}^{-1}+5^1{.7}^{-1}{+}_{\dots }\right]$ upto 20 twenty terms is

• A. $\frac{800}{7}$
• B. $\frac{580}{7}$
• C. $\frac{780}{9}$
• D. $\frac{680}{7}$

Answer 1

The correct option is A $\frac{800}{7}$

$2\left[7^{-1}+3^1{.7}^{-1}+5^1{.7}^{-1}+....\right]$ upto $20$ terms
$=2\left[\frac{1}{7}+\frac{3}{7}+\frac{5}{7}+...\right]$ upto $20$ terms
$=\frac{2}{7}\left[1+3+5+...\right]$ upto $20$ terms
$=\frac{2}{7}\left[\frac{20}{2}\left\{2\times 1+\left(20-1\right)2\right\}\right]$ (since it is an A.P)
$=\frac{2}{7}\left[\frac{20}{2}\left(2+38\right)\right]$
$=\frac{20}{7}\times 40$
$=\frac{800}{7}$