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Find the sum of the infinite geometric s...

Find the sum of the infinite geometric series `(1-1/3+1/3^(2)-1/3^(3)+...oo)`.

A

`3/4`

B

`3/2`

C

`1/4`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
A
The given series is an infinite geometric series in which
`a=1, r=-1/3` and `|r|=1/3 lt 1`
Hence, the sum of the given infinite geometric series is
`S=a/((1-r))=1/((1+1/3))=1/((4/3))=3/4`.
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