Question

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it:

`1/2, 1/4, 1/8, 1/16`, ...

Answer 1

`1/2, 1/4, 1/8, 1/16`, ...

Here, `"a" = 1/2, "r" = (1/4)/(1/2) = 1/2`

Since, | r | = `|1/2| < 1`

∴ Sum to infinity exists.

Sum to infinity = `"a"/(1 - "r") = (1/2)/(1 - 1/2)` = 1.