Question

Find the sum the infinite G.P.: $\frac{2}{3}-\frac{4}{9}+\frac{8}{27}-\frac{16}{21}+........$

• A. $\frac{2}{5}$
• B. $\frac{3}{5}$
• C. $\frac{19}{27}$
• D. $\frac{8}{5}$

Answer 1

Answer: (A)

$\frac{2}{5}$

We know, $S_{\infty }=\frac{a}{1-r}$
From the given series, $a=\frac{2}{3},r=-\frac{2}{3}$
$\therefore S_{\infty }=\frac{\frac{2}{3}}{1-(-\frac{2}{3})}$

$\Rightarrow \frac{\frac{2}{3}}{1+\frac{2}{3}}$

$\Rightarrow \frac{\frac{2}{3}}{\frac{5}{3}}$

$\Rightarrow \frac{2}{5}$