Question

How do you find the sum of the infinite geometric series -3, -3/2, -3/4, -3/8?

Answer 1

The sum of this sequence is `-6`

Explanation:

To find the sum of an infinite geometric sequence we use the formula:

`S=a_1/(1-q)`

First we have to find `q` to see if the sequence is convergent:

`q=-3/2:(-3)=1/2`

`abs(q)<1`, so the sequence is convergent. We can calculate the sum:

`S=a_1/(1-q)=(-3)/(1-1/2)=-3/(1/2)=-3*2=-6`