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 C_(0)-C_(2)+C_(4)-C_(6)+........ Where C_(r)=nC_(r)

Find the sum 1C_(0)+2C_(1)+3C_(2)+...+(n+1)C_(n), where C_(r)=^(n)C_(r)

Find the sum sum_(r=0)^n(-1)^r*(""^nC_r)/(""^(r+3)C_r)

Find the value of the determinant |(.^(n)C_(r-1),.^(n)C_(r),(r+1)^(n+2)C_(r+1)),(.^(n)C_(r),.^(n)C_(r+1),(r+2)^(n+2)C_(r+2)),(.^(n)C_(r+1),.^(n)C_(r+2),(r+3)^(n+2)C_(r+3))|

sum_(r=1)^(6)6C_(r)

The sum of the series sum_(r=0) ^(n) ""^(2n)C_(r), is

Find the sum sum_(i=0)^(r)*^(n_(1))C_(r-i).^(n_(2))C_(i)

Find the value of .^(n)C_(r)+.^(n-1)C_(r)+......+.^(r)C_(r)