The coefficient of x ⁹⁹ in the expansion of ( x -1)( x -2)( x -3) . . (x-100) is

Step-by-step solution

Coefficient of x^1 in [(x-1)(x-2) . or . (x^2-3 x+2 ) ]=-3=-1-2=-(1+2) Coefficient of x^2 in [(x-1)(x-2)(x-3) . or (x^3-6 x^2+5 x . aligned & -6)] & =-6=-[1+2+3] aligned Coefficient of x^3 in [(x-1)(x-2)(x-3)(x-4) or aligned & . ( x ^4-10 x ^3-29 x ^2-11 x +24 ) ] & =-10=-[1+2+3+4] aligned Coefficient of x ⁹⁹ in [( x -1)( x -2) .( x -100)]=-[1+2+3+ . .+100]= -100(100+1) 2 =-5050 .