What is the coefficient of `x^(4)` in the expansion of `(1+2x+3x^(2)+4x^(3)+….)^(1//2)` ?A. `1//4`B. `1//16`C. 1D. `1//128`

What is the coefficient of `x^(4)` in the expansion of `(1+2x+3x^(2)+4

1.	What is the coefficient of `x^(4)` in the expansion of `(1+2x+3x^(2)+4x^(3)+….)^(1//2)` ?A. `1//4`B. `1//16`C. 1D. `1//128`
Answer» Correct Answer - C Consider `(1+2x+3x^(2)+4x^(3)+…)^(1//2)=(1-x^(-2))^(1//2)` As we know that `(1-x)^(-2)=1+2x+3x^(2)+4x^(3)+….` `rArr" "(1-x)(-1)=1+x+x^(2)+x^(3)+x^(4)+….` `therefore" Required coefficient of "x^(4)" is 1 "`

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