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

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Answer 1 · 2014-08-29T14:44:57

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.

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