How do you find the sum of the infinite geometric series 1/5+1/10+1/20+1/40+...?

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Answer 1 · 2018-04-08T16:51:37

Sum of infinite series is #2/5#

Let sum of infinite series be #S# i.e.

#S=1/5+1/10+1/20+1/40+........#

then #1/2S=1/10+1/20+1/40+1/80+......#
(note that we have multiplied by common ratio #1/2#)

Subtracting latter from former, we get

#S-1/2S=1/5#

or #S/2=1/5#

i.e. #S=2/5#