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If |x|<1, then find the coefficient of x...

If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+2x+3x^2+4x^3+)^(1//2)dot`

Text Solution

Verified by Experts

The correct Answer is:
1
Since `1+2z+3x^(2)+4x^(3)+"……"oo= (1+x)^(2)`, we have
`(1+2x+3x^(2)+4x^(3)+"……"oo)^(1//2) = [(1-x)^(-2)]^(1//2)`
`= (1-x)^(-1)`
`= 1+x+x^(2)+"…."+x^(n) + "…."oo`
Therefore, the coefficient of `s^(n)` is `1`.
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