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Find the value of x , for which 1//(sqrt...

Find the value of `x ,` for which `1//(sqrt(5+4x))` can be expanded as infinite series.

Text Solution

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We have `(1)/(sqrt(5)+4x) = (1)/(sqrt(5) xx sqrt(1+(4x)/(5)))`
`= 5^(-1//2)(1+4/(5)x)^(-1//2)`
This can be expanded as infinite series, only if `|4/5x| lt 1`
or `|x| lt 5/4`.
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