Question

How do you find the sum of the infinite geometric series given `6-2.4+0.96-...`?

Answer 1

`30/7 ~= 4.28571`

Explanation:

`S= 6-2.4+0.96- ....`

To find the common ratio: `r=-2.4/6 = -0.4`

Check: `-2.4 xx (-0.4) = +0.96` [OK}

The sum of an infinite geometric sequence where `abs r <1` is `a/(1-r)` where `a` is the first term and `r` is the common ratio.

`:. S= 6/(1-(-0.4))`

`= 6/1.4 = 60/14 = 30/7 ~= 4.28571`