Question

How do you find the sum of the following infinite geometric series, if it exists. 2 + 1.5 + 1.125 + 0.8437 +…?

Answer 1

Sum of the given infinite geometric series is `8`

Explanation:

The ratio, `r` between successive geometric terms is
`color(white)("XXX")(1.5)/2=1.125/1.5=...=0.75`

The initial term `a_1` is given as `2`

Since `abs(r) < 1`
this infinite geometric series has a sum given by the formula
`color(white)("XXX")(a_1)/(1-r)`

In this case
sum `= (2)/((1-0.75)) = 2/0.25 = 8`