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

Question

18641 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-25T20:46:51

As Alan P. indicated, this question has to be modified. I'm gonna assume that it is #-1/8# instead of #+1/8#

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 = #-1/2#

The ratio is therefore #-1/2#. The formula for the sum of an infinite geometric series is #s_oo = a/(1 - r)#

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

#s_oo = 1/(3/2)#

#s_oo = 2/3#

Exercises

Find the sum of the following infinite geometric series: 2, #6/5#, #18/25#, ...
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.