If `n > 3,` then `x y C_0-(x-1)(y-1)C_1+(x-2)(y-2)C_2-(x-3)(y-3)C_3+..............+(-1)^n(x-n)(y-n)C_n,` equals

If n gt 3 , then xyz^(n)C_(0)-(x-1)(y-1)(z-1)""^(n)C_(1)+(x-2)(y-2)(z-2)""^(n)C_(2)- (x-3)(y-3)(z-3)""^(n)C_(3)+…..+(-1)^(n)(x-n)(y-n)(z-n)""^(n)C_(n) equals :

Show : x-^(n)C_(1)(x+y)+^(n)C_(2)(x+2y)-^(n)C_(3)(x+3y)+....=0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)-(C_(1))/(2)+(C_(2))/(3)-......+(-1)^(n).(C_(n))/(n+1)=(1)/(n+1)

tan^(-1)(C_(1)x-y)/(c_(1)+c_(3)c_(2))+..+tan^(-1)(1)/(c_(n)) is equal top

The number of ways of choosing triplet (x , y ,z) such that zgtmax{x, y} and x ,y ,z in {1,2,.......... n, n+1} is (A) .^n+1C_3+^(n+2)C_3 (B) n(n+1)(2n+1)//6 (C) 1^2+2^2+..............+n^2 (D) 2(.^(n+2)C_3)-(.^(n+1)C_2)

The number of ways of choosing triplet (x , y ,z) such that zgtmax{x, y} and x ,y ,z in {1,2,.......... n, n+1} is (A) .^n+1C_3+^(n+2)C_3 (B) n(n+1)(2n+1)//6 (C) 1^2+2^2+..............+n^2 (D) 2(.^(n+2)C_3)-(.^(n+1)C_2)

Show that (n !)/(x(x+1)(x+2)...(x+n))=(""^(n)C_(0))/(x)-(""^(n)C_(1))/(x+1) + (""^(n)C_(2))/(x+2)-(""^(n)C_(3))/(x+3) + ...+ ((-1)^(n)""^(n)C_(n))/(x+n) .