If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+x+x^2+)^2dot`
If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+x+x^2+)^2dot`
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Correct Answer - `(n+1)`
Given expression is
`(1+x+x^(2)+"…..")^(2)=[(1-x)^(-1)]^(2)`
`= (1-x)^(-2)`
`= 1+2x+3x^(2)+4x^(3)+"……"+nx^(n-1)`
Therefore the coefficient of `x^(n)` is `n+1`.
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