Prove that `Delta [[1,1,1],[nC1, (n+1)C1,(n+2)C1],[(n+1)C2 , (n+2)C2, (n+3)C2]] = 1 `

If 3^n is a factor of the determinant |{:(1,1,1),(.^nC_1,.^(n+3)C_1,.^(n+6)C_1),(.^nC_2, .^(n+3)C_2, .^(n+6)C_2):}| then the maximum value of n is ……..

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 ^n C_0^n C_0-^(n+1)C_1^n C_1+^(n+2)C_2^n C_2-=(-1)^ndot

Prove that ^n C_0 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2-=(-1)^ndot

Prove that ^n C_0 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2-=(-1)^ndot

The value of |1 1 1^n C_1^(n+2)C_1^(n+4)C_1^n C_2^(n+2)C_2^(n+4)C_2| is

Prove that "^(2n)C_1 + ^(2n)C_3 + .... + ^(2n)C_(2n-1) = 2^(2n-1)

|{:(1,1,1),(""^(n)c_1,""^(n+1)c_1,""^(n+2)c_1),(""^(n+1)c_2,""^(n+2)c_2,""^(n+3)c_2):}|=1

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