Question

How do you find the sum of the infinite geometric series 3 - 2 + 4/3 - 8/9 + ...?

Answer 1

The sum of this series is `1 4/5`

Explanation:

`a_1=3`

`q=(a_2)/(a_1)=-2/3`

Since `|q|<1`, the sequence is convergent, so we can calculate the sum using:

`S=a_1/(1-q)=3/(1-(-2/3))=3/(1+2/3)=3/(5/3)=3*3/5=9/5=1 4/5`