If `(1+x)^n=C_0+C_1x+C2x2++C_n x^n , t h e n 'C_0-(C_0+C_1+)+(C_0+C_1+C_2)-(C_0+C_1+C_2+C_3)+(-1)^(n-1)(C_0+C_1+ C_(n-1))',w h e r e n` is

If (1+x)^n=C_0+C_1x+C2x2++C_n x^n , n in N ,t h e nC_0-C_1+C_2-+(-1)^(n-1)C_(m-1), is equal to (mltn)

If (1+x)^n=C_0+C_1x+C_2x^2++C_n x^n ,t h e nC_0C_2+C_1C_3+C_2C_4++C_(n-2)C_n= ((2n)!)/((n !)^2) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((n-2)!(n+2)!) d. none of these

.^((n-1)C_(r) + ^((n-1)) C_((r-1)) is

Prove that ^n C_0^n C_0-^(n+1)C_1^n C_1+^(n+2)C_2^n C_2-=(-1)^ndot

(C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n)= (C_0C_1C_2.....C_(n-1) (n+1)^n)/(n!)

if (1 + C_(1)/C_(0))(1 + C_(2)/C_(1)) (1 + C_(3)/C_(2)) ...... (1 + C_(n)/C_(n - 1))is

Prove that C_0-2^2C_1+3^2C_2-4^2C_3+...+(-1)^n(n+1)^2xxC_n=0w h e r eC_r=^n C_r .

If (1 - x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + ......... + C_(n)x^(n) , then the value of 1.C_(1) + 2.C_(3) + 3.C_(3) + ......... + n.C_(n) =

Prove that "^n C_0^(2n)C_n-^n C_1^(2n-1)C_n+^n C_2xx^(2n-2)C_n++(-1)^n^n C_n^n C_n=1.

If ""^(2n)C_(3) : ""^(n) C_(3)= 11 : 1 then n is