Coefficient of x^{19} in the polynomial (x-1) | vedclass

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Question

No. of factors is $=20$

Polynomial $=x^{20}-x^{19}\left(1+2+2^{2} \ldots+2^{19}\right)+\ldots \ldots$

Coeff. of $x^{19}=-\left(1+2+2^{2}+\ldots+

Vedclass · Accepted Answer

$-(2^{20} -1)$

Vedclass · Answer

No. of factors is $=20$

Polynomial $=x^{20}-x^{19}\left(1+2+2^{2} \ldots+2^{19}\right)+\ldots \ldots$

Coeff. of $x^{19}=-\left(1+2+2^{2}+\ldots+2^{19}\right)$

$=-\left(\frac{1-2^{20}}{1-2}\right)=-\left(2^{20}-1\right)$

Coefficient of $x^{19}$ in the polynomial $(x-1) (x-2^1) (x-2^2) .... (x-2^{19})$ is

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