help 29

If you think about how this would expand, x^99 can only be created when 99 xs multiply, times a constant.

Because there are 100 different constants (-1 to -100), the coefficent will be the sum of an arithmetic sequence.

$-1\times x^{99}-2\times x^{99}-3\times x^{99}-...-100\times x^{99}$

$S_{100}=\frac{100}{2}(-1-100)$

$S_{100}=-5050$

Coefficient will be -5050.