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` .

Prove that C_(0)2^(2)C_(1)+3C_(2)4^(2)C_(3)+...+(-1)^(n)(n+1)^(2)C_(n)=0 where C_(r)=nC_(r)

Prove that C_(0)-2^(2)C_(1)+3^(2)C_(2)-4^(2)C_(3)+...+(-1)^(n)(n+1)^(2)xx C_(n)=0 where C_(r)=^(n)C_(r)

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

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

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

If (1+x)^n=C_0+C_1x+C_2x^2+…+C_nx^n show that C_1-2C_2+3C_3-4C_4+…+(-1)^(n-1) n.C_n=0 where C_r=^nC_r .

Given that C_1+2C_2x+3C_3x^2++2nC_(2n)x^(2n-1)=2n(1+x)^(2n-1), w h e r eC_r=(2n)!//[r !(2n-r)!]; r=0,1,2, ,2n , then prove that C1 2-2C2 2+3C3 2--2n C2n2=(-1)^nn C_ndot

Find the sum 1xx2xxC_1+2xx3C_2+ +n(n+1)C_n ,w h e r eC_r=^n C_rdot

Find the sum 1C_0+2C_1+3C_2++(n+1)C_n ,w h e r eC_r=^n C_rdot

Find the sum 1C_0+2C_1+3C_2++(n+1)C_n ,w h e r eC_r=^n C_rdot