Question

The sum of the infinite terms of $1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\dots$, will be.

• A. $\frac{35}{16}$
• B. $\frac{16}{35}$
• C. $\frac{15}{16}$
• D. $\frac{7}{4}$

Answer 1

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

Let $S=1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\dots$.............{i}
$\therefore \frac{S}{5}=\frac{1}{5}+\frac{4}{5^2}+\frac{7}{5^3}+\frac{10}{5^4}+\dots$..........{ii}
Now, Subtracting {ii} from {i} by shifting one place, we get
$\frac{4S}{5}=1+\frac{3}{5}(1+\frac{1}{5}+\frac{1}{5^2}+\dots )=1+\frac{3}{5}\frac{1}{1-\frac{1}{5}}=1+\frac{3}{4}=\frac{7}{4}$
$\therefore S=\frac{35}{16}$
Hence, option 'A' is correct.