Question

The sum (upto two decimal places) of the infinite series $\frac{7}{17}+\frac{77}{17^2}+\frac{777}{17^3}+.......$ is

• A. 1.06
• B. 2.06
• C. 3.06
• D. 4.06

Answer 1

Answer: (A)

$S=\frac{7}{17}+\frac{77}{17^2}+\frac{777}{17^3}+.......$
$\frac{S}{17}=\frac{7}{17^2}+\frac{77}{17^3}+\frac{777}{17^4}+........$
Subtracting both the above results, we get,
$\frac{16}{17}S=\frac{7}{17}+\frac{70}{17^2}+\frac{700}{17^3}+.......$
$\left(InfiniteG.P.withr=\frac{10}{17}\right)$
$\frac{16}{17}S=\frac{\frac{7}{17}}{1-\frac{10}{17}}=\frac{\frac{7}{17}}{\frac{7}{17}}=1$
$S=\frac{17}{16}$