Question

Calculate the sum of the infinite series

Answer 1

A. 40/3 hope thats helpful

Answer 2

`(40)/(3)`

Explanation:

Here a= 20, r = -1/2

Here, the absolute value of r is 1/2 which is less than 1. So, the series converges.

The sum of an infinite geometric series is given by

S =
`(a)/(1-r)`

Substituting the values in the above equation, we have

`S = (20)/(1-(-1/2)) =(20)/(3/2) =(40)/(3)`

∴ The sum of the given infinite series is 40/3