The coefficient of $x^{99}$ in the polynomial $\left(x-1\right)\left(x-2\right)\left(x-3\right)...\left(x-100\right)$ is

If we multiply the brackets and take $x$ from each bracket except one, that is, we take $x$ from $99$ brackets and the constant term from the last bracket we will have $x^{9}9$

So coefficient of $x^{9}9$ will be sum of all the constant terms taken once in this manner.