The coefficient of x n in 1-x-2 x2-3 x3- - -n xn2 is -

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Special Integrals - 2

The coefficie...

Question

The coefficient of xⁿin (1+x+2x²+3x³+.....+nxⁿ)²is ?

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X^{n}

{(1 + X + 2 X^{2} + 3 X^{3} + . . . . + n X^{n})}^{2}

x^{n}

(1 + x + 2 x^{2} + 3 x^{3} + . . . . . + n x^{n})

Coefficient of $x^{18} i n (1 + x + 2 x^{2} + 3 x^{3} + . . . . . . . + 18 x^{18}$ is equal to

a

b

x^{3}

(1 + x + 2 x^{2} + 3 x^{3})^{4}

(1 + x + 2 x^{2} + 3 x^{3} + 4 x^{4})^{4}

\frac{6 a}{b}

x^{r}

1 + (1 + x) + (1 + x)^{2} + . . . . . . + (1 + x)^{n}

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