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What is the sum of the infinite geometric series #1/8-1/4+1/2-1+…# ?

1 Answer

Aug 29, 2014

The posted geometric series diverges since its r-value is #-2#, whose absolute value is greater than or equal to 1.

By using summation notation, we can write
#1/8-1/4+1/2-1=sum_{n=0}^{infty}1/8(-2)^n#,
where #a=1/8# and #r=-2#.

Since #|r|=|-2|=2\geq1#, the series diverges by Geometric Series Test.

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