The condition that `x^(n+1)-x^(n)+1` shall be divisible by `x^(2)-x+1` is that :

Show that (1+x)^(n) - nx-1 is divisible by x^(2) for n gt N

Prove the following by the principle of mathematical induction: \ x^(2n-1)+y^(2n-1) is divisible by x+y for all n in NNdot

Statement 1: 2^(33)-1 is divisible by 7. Statement 2: x^(n)-a^(n) is divisible by x-a , for all n in NN and x ne a .

Statement 1: 3^(2n+2)-8n-9 is divisible by 64 ,AAn in Ndot Statement 2: (1+x)^n-n x-1 is divisible by x^2,AAn in Ndot

If n is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that (x+1)^n-x^n-1 is divisible by x^3+x^2+xdot

If n is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that (x+1)^n-x^n-1 is divisible by x^3+x^2+xdot

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)

The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

Statement -1 for all natural numbers n , 2.7^(n)+3.5^(n)-5 is divisible by 24. Statement -2 if f(x) is divisible by x, then f(x+1)-f(x) is divisible by x+1,forall x in N .

If n > 1 is an integer and x!=0, then (1 +x)^n-nx-1 is divisible by