How do you find the sum of the infinite geometric series 1-1/2+1/4+1/8?

Jan 25, 2016

As Alan P. indicated, this question has to be modified. I'm gonna assume that it is $- \frac{1}{8}$ instead of $+ \frac{1}{8}$

Explanation:

First you must find r, the common ratio.

You find this with the following formula: r = ${t}_{2} / {t}_{1}$

r = (-1/2)/1)

r = $- \frac{1}{2}$

The ratio is therefore $- \frac{1}{2}$. The formula for the sum of an infinite geometric series is ${s}_{\infty} = \frac{a}{1 - r}$

s_oo = 1 / ( 1 - (-1/2)#

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

${s}_{\infty} = \frac{2}{3}$

Exercises

1. Find the sum of the following infinite geometric series: 2, $\frac{6}{5}$, $\frac{18}{25}$, ...

2. Assume that a pendulum swings forever. The second swing measures 63 cm. The pendulum's distance diminishes by a third each time. Find the total distance covered by the pendulum rounded to 3 decimals.