Question

How do you find the sum of the infinite geometric series 2 + 1.5 + 1.125 + 0.8437 +…?

Answer 1

`2+1.5+1.125+0.84375+ ... = 8`

Explanation:

The sum of an infinite geometric series with initial value `a_1` and ratio `r, abs(r) < 1` is given by the formula:
`color(white)("XXX")Sigma a_i = a_1/(1-r)`

Since for the given series:
`color(white)("XXX")1.5/2 = 1.125/1.5 = 0.84375/1.125 = 0.75`
`r=0.75`

and
`color(white)("XXX")Sigma a_i = 2/(1-0.75) = 8`

Note: since we were told this was a geometric series I felt justified in replacing `0.8437` with `0.84375`