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Find the sum of the infinite geomwtric s...

Find the sum of the infinite geomwtric series `((-5)/4+5/16-5/64+...oo)`.

Text Solution

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In the given infinite geometric series, we have
`a=(-5)/4, r=(5/16xx4/(-5))=-1/4` and `|r|=1/4 lt 1`.
Hence, the sum of the given infinite geometric series is
`S=a/((1-r))=((-5//4))/((1+1/4))=((-5)/4xx4/5)=-1`.
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