How do you find the sum of the infinite geometric series 5/4-1/4+1/20-1/100+...?

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Answer 1 · 2016-02-07T21:38:58

First, find the common ratio, r.

#r = t_2/t_1#

#r = (-1/4)/(5/4)#

#r = -1/5#

Now, we know all we need to know to find the sun, which can be found using the formula #S_oo = a/(1 - r)#

#S_oo = (5/4)/(1 - (-1/5))#

#S_oo = (5/4) / (6/5)#

#S_oo = 25/24#

The sum of the series is #25/24#