Find the sum `C_0-C_2+C_4-C_6+ ,w h e r eC_r=^6C_r=^n C_r` .

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

Find the sum sum_(r=0)^n^(n+r)C_r .

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 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

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

Show that 4C_0 +4C_1 +4C_2 +.....+4C_n>(2^(4n))/(n^3),w h e r e^n C_r=n !//[r !(n-r)!]dot

Find the sum of sum_(r=1)^n(r^n C_r)/(n C_(r-1) .

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

If (1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a= (^n C_2)^2 b. ^n C_rdot^n C_(r+1) c. ^2n C_r d. ^2n C_(r+1)