Question

What is the sum of the infinite geometric series?
-3-3/2-3/4-3/8-3/16-....

Answer 1

- 6

Explanation:

The sum to infinity of a geometric series is calculated as

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

where a is the first term and r the common ratio

Here a = - 3 and r = -
`(3)/(2)` ÷ - 3 =
`(1)/(2)`, thus

S( infinity ) =
`(-3)/(1-(1)/(2) )` =
`(-3)/((1)/(2) )` = - 6