Prove that `(nC_0)/1+(nC_2)/3+(nC_4)/5+(nC_6)/7+.....= 2^n/(n+1).`

Prove that (""^nC_r)/(""^nC_(r-1))=(n-r+1)/r

Prove that (2nC_0)^2-(2nC_1)^2+(2nC_2)^2+.....+(2nC_2n)^2=(-1)^n2nC_n

Prove that ""^nC_r+^nC_(r-1)=^(n+1)C_r

Prove that (""^nC_1)/(""^nC_0)+2*(""^nC_2)/(""^nC_1)+3*(""^nC_3)/(""^nC_2)+...+n*(""^nC_n)/(""^nC_(n-1))=frac{n(n+1)}{2}

Prove that 2*""^nC_0+2^2*(""^nC_1)/2+2^3*(""^nC_2)/3+...2^(n+1)*(""^nC_n)/(n+1)=(3^(n+1)-1)/(n+1)

Prove that (2nC_(1))^(2)+2.(2nC_(2))^(2)+3*(2nC_(3))^(2)+......+2n*(2nC_ (2n))^(2)=((4n-1)!)/((([(2n-1)!])^(2))

Prove that: (1)/(2)nC_(1)-(2)/(3)nC_(2)+(3)/(4)nC_(3)-(4)/(5)nC_(4) +....+((-1)^(n+1)n)/(n+1)*nC_(n)=(1)/(n+1)

Prove that (2nC_0)^2+(2nC_1)^2+(2nC_2)^2-+(2nC_(2n))^2=(-1)^n2nC_ndot

Prove that ^nC_0 "^(2n)C_n-^nC_1 ^(2n-2)C_n +^nC_2 ^(2n-4)C_n =2^n

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to