Question

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

Answer 1

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.