Question

How do you find the sum of the infinite geometric series 1/4 + 1/8 + 1/16 + 1/32 + ..?

Answer 1

`1/2`

Explanation:

In a geometric series, we multiply by some number `r` to get to the next term.

The trick is to find this number `r`. If `|r| < 1` then you can use the following expression to find the sum:
`a/(1-r)`, where `a` is the first term of the series.

we know this:
`1/4 * r = 1/8`
`r = 1/8 * 4`
`r = 1/2`

Since `|r| < 1`, we may continue...
`a=1/4`

`a/(1-r)=(1/4)/(1-1/2)`
`a/(1-r)=(1/4)/(1/2)`
`a/(1-r)=(1/4)-:(1/2)`
`a/(1-r)=(1/4)*(2)`

`a/(1-r)=1/2`