# How do you find the sum of the infinite geometric series given 1/4+1/6+2/18+ ...?

Nov 13, 2016

The sum is $\frac{3}{4}$.

#### Explanation:

Use the formula ${s}_{\infty} = \frac{a}{1 - r}$, where $r = {t}_{2} / {t}_{1}$.

$r = {t}_{2} / {t}_{1}$

$r = \frac{\frac{1}{6}}{\frac{1}{4}} = \frac{1}{6} \times 4 = \frac{2}{3}$

$\therefore {s}_{\infty} = \frac{\frac{1}{4}}{1 - \frac{2}{3}}$

${s}_{\infty} = \frac{\frac{1}{4}}{\frac{1}{3}}$

${s}_{\infty} = \frac{3}{4}$

Hopefully this helps!