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  4. The coefficient of x19 in the expression (x-1)(x-22)(x-32) (x-202) must be

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Q. The coefficient of $x^{19}$ in the expression $(x-1)\left(x-2^2\right)\left(x-3^2\right)$ $\left(x-20^2\right)$ must be

Binomial Theorem

Solution:

Co-efficient of $x^{19}$ in expression $=-\left(1^2+2^2+3^2+\ldots \ldots . .+20^2\right)=-2870$