Question

?How do you find the sum of the infinite geometric series 4 + 0.4 + 0.04 + ....?

Answer 1

`Sum=40/9`

Explanation:

`a_2/a_1=0.4/4=4/40=1/10`
`a_3/a_2=0.04/0.4=4/40=1/10`
`implies r=1/10` and `a_1=4`

Sum of infinite geometric series is given by
`Sum=S=a_1/(1-r)=4/(1-1/10)=40/(10-1)=40/9`
`implies Sum=40/9`