^2nC_(2)+^(2n)C_(4)+....+^(2n)C_(2n)=

Prove that : (1+""^nC_1+""^nC_2+""^nC_3+...+""^nC_n)^2=1+""^(2n)C_1+""^(2n)C_2+""^(2n)C_3+...+""^(2n)C_(2n)

The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to

The expression nC_(0)+4*nC_(1)+4^(2)nC_(2)+.....4^(n^(n))C_(n), equals

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

Prove that ^nC_(0)^(2n)C_(n)-^(n)C_(1)^(2n-1)C_(n)+^(n)C_(2)xx^(2n-2)C_(n)++(-1)^(n)sim nC_(n)^(n)C_(n)=1

Prove that "^nC_r+2 ^(n)C_(r-1)+ ^(n)C_(r-2) = ^(n+2)C_r .

The middle term in the expansion of ((2x)/(3)-(3)/(2x^(2)))^(2n) is ^(2n)C_(n) b.(-1)^(n)2nC_(n)x^(-n) c.^(2n)C_(n)x^(-n)d .none of these

Prove that : ""^(n)C_(0).""^(2n)C_(n)-""^(n)C_(1).""^(2n-2)Cn_(n)+""^(n)C_(2).""^(2n-4)Cn_(n)+......=2^n