+257 Find the co- efficient of x^99 in (x-1)*(x-2)*.........................(x-100)
+561 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.
