Question

. Find the sum of the infinite series, if it exists.

-270+135-67.5+⋯

Answer 1

-180

Explanation:

135/-270 = -1/2

67.5/135 = -1/2

The series is an infinite geometric series with r = -1/2

Since -1 < |r| < 1, the series has a sum

and equals a/(1 - r) a = -270

S = a/(1 - r) = -270/(1 + 1/2) = -270/(3/2) = -180