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Q.
The coefficient of $x^{19}$ in the polynomial $(x-1)(x-2)\left(x-2^{2}\right) \ldots\left(x-2^{19}\right)$ is
Sequences and Series
Solution:
The coefficient of $x^{19}$ in the polynomial
$(x-1)(x-2)\left(x-2^{2}\right) \ldots\left(x-2^{19}\right)$ is
$-\left(1+2+2^{2}+\ldots .+2^{19}\right)$
$=-1\left(\frac{2^{20}-1}{2-1}\right)=1-2^{20}$