Question

Sum to infinity of the series $1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+...=$

• A. $\frac{16}{35}$
• B. $\frac{35}{16}$
• C. $\frac{1}{8}$
• D. $\frac{35}{8}$

Answer 1

The correct option is B $\frac{35}{16}$

$S=1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+.....\infty$

$-$

$\frac{S}{5}=\frac{1}{5}+\frac{4}{5^2}+\frac{7}{5^3}+.....\infty$

$\frac{4S}{5}=1+\frac{3}{5}+\frac{3}{5^2}+\frac{3}{5^3}+......\infty$

$\frac{4S}{5}=1+3[\frac{1}{5}+\frac{1}{5^2}....\infty ]$

$\frac{4S}{5}=1+\frac{3}{5}\left[\frac{1}{1-1/5}\right]$

$\frac{4S}{5}=1+\frac{3}{4}$

$\frac{4S}{5}=\frac{7}{4}$

$S=\frac{35}{16}$