How do you find the sum of the infinite geometric series 1/4 + 1/8 + 1/16 + 1/32 + ..?

1 Answer
Edric Y.
Nov 12, 2015

#1/2#

Explanation:

In a geometric series, we multiply by some number #r# to get to the next term.

The trick is to find this number #r#. If #|r| < 1# then you can use the following expression to find the sum:
#a/(1-r)#, where #a# is the first term of the series.

we know this:
#1/4 * r = 1/8#
# r = 1/8 * 4#
# r = 1/2#

Since #|r| < 1#, we may continue...
#a=1/4#

#a/(1-r)=(1/4)/(1-1/2)#
#a/(1-r)=(1/4)/(1/2)#
#a/(1-r)=(1/4)-:(1/2)#
#a/(1-r)=(1/4)*(2)#

#a/(1-r)=1/2#

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