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+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+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

Find the sum 3^n C_0-8^n C_1+13^n C_2 - 18^n C_3+..

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) =

If (1+x)^n=sum_(r=0)^n^n C_r , show that C_0+(C_1)/2++(C_n)/(n+1)=(2^(n+1)-1)/(n+1) .

If (1-x)^(-n)=a_0+a_1x+a_2x^2++a_r x^r+ ,t h e na_0+a_1+a_2++a_r is equal to (a) (n(n+1)(n+2)(n+r))/(r !) (b) ((n+1)(n+2)(n+r))/(r !) (c) (n(n+1)(n+2)(n+r-1))/(r !) (d)none of these

If n >2, then prove that C_1(a-1)-C_2xx(a-2)++(-1)^(n-1)C_n(a-n)=a ,w h e r eC_r=^n C_rdot

(n+2)nC_0(2^(n+1))-(n+1)nC_1(2^(n))+(n)nC_2(2^(n-1))-.... is equal to

If (1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n , then show that the sum of the products of the coefficients taken two at a time, represented by sumsum_(0lt=iltjlt=n) "^nc_i "^n c_j is equal to 2^(2n-1)-((2n)!)/ (2(n !)^2)

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