Find the sum of the following geometric series 1/2 + (-1/4) + 1/8 + (-1/16) + ...

Expert Answers
justaguide eNotes educator| Certified Educator

The numbers 1/2, (-1/4), 1/8, (-1/16)... form a geometric series with the first term (1/2) and the common ratio `(-1/4)/(1/2) = -1/2`

The sum of the first n terms of a geometric series is `a*(r^n - 1)/(r - 1)`

If r < 1, `S_oo = a/(1 - r)`

For the given series, `S_oo = (1/2)/(1/2 + 1) = 1/3`

The value of `1/2 + (-1/4) + 1/8 + (-1/16) + ... = 1/3`

justinyu | Student

First term is 1/2 and the common ratio is -1/2
So ∑∞ = a/(1-r) = 1/2/(1+1/2) = 1/3