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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`, ...
Solution
`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.
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