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Find the sum of the infinite geometric s...

Find the sum of the infinite geometric series `(1+1/3+1/9+1/27+...oo)`.

Text Solution

Verified by Experts

In the given infinite geometric series, we have
`a=1` and `r=1/3` such that `|r|=1/3 lt 1`.
Hence, the sum of the given infinite series is
`S=1/((1-r))=1/((1-1/3))=1/((2/3))=3/2`.
Hence, the required sum is `3/2`.
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