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

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

Prove that, C_(0) *""^(2n)C_(n)-C_(1)*""^((2n-2))C_(n)+C_(2) *""^((2n-4))C_(n)-…..=2^(n)

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

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0) *""^(2n)C_(n) - C_(1) *""^(2n-2)C_(n) + C_(2) *""^(2n-4) C_(n) -…= 2^(n)

Prove that ^n C_0 ^(2n)C_n- ^n C_1 ^(2n-2)C_n+ ^n C_2^(2n-4)C_n-=2^ndot

Evaluate .^(n)C_(0).^(n)C_(2)+.^(n)C_(1).^(n)C_(3)+.^(n)C_(2).^(n)C_(4)+"...."+.^(n)C_(n-2).^(n)C_(n) .