Q. $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + \ldots to\ \infty$ is
A) $\frac{16}{35}$
B) $\frac{11}{8}$
C) $\frac{35}{16}$
D) $\frac{7}{16}$
Explanation
(c)
Using, $S_{\infty} = \frac{a}{1 - r} + \frac{dr}{(1 - r)^{2}}$
Here, $a = 1,\ \ r = \frac{1}{5},\ \ d = 3$
$\therefore S_{\infty} = \frac{1}{1 - \frac{1}{5}} + \frac{3 \times \frac{1}{5}}{\left( 1 - \frac{1}{5} \right)^{2}}$
$= \frac{5}{4} + \frac{3}{5 \times \frac{16}{25}}$
$= \frac{5}{4} + \frac{15}{16} = \frac{35}{16}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.