Question

The infinite sum $\sum _{n=1}^{\infty }\left(\frac{5^n+3^n}{5^n}\right)$ is equal to:

• A. $\frac{3}{2}$
• B. $\frac{3}{5}$
• C. $\frac{2}{3}$
• D. None of these

Answer 1

Answer: (D)

(i) $\sum _{n=1}^{\infty }\left(1+{\left(\frac{3}{5}\right)}^n\right)=1+\frac{3}{5}+{\left(\frac{3}{5}\right)}^2+\dots \infty$
(ii) $S_{\infty }=\frac{a}{1-r}$, where $a$ is the first term and $r$ is the common ratio.