Binomial theorem for any positive integer n

Binomial theorem for any index

Introduction||Binomial theorem for positive index , Illustration

Let A,B be two matrices such that they commute.Show that for any positive integer n,(AB)^(n)=A^(n)B^(n)

Let A,B be two matrices such that they commute.Show that for any positive integer n,AB^(n)=B^(n)A

If A is a square matrix such that |A| = 2 , then for any positive integer n, |A^(n)| is equal to

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

Prove,by mathematical induction,that x^(n)+y^(n) is divisible by x+y for any positive odd integer n.

Binomial theorem General observations

Use factor theorem to prove that (x+a) is a factor of (x^(n)+a^(n)) for any odd positive integer n .

Use factor theorem to verify that y+a is factor of y^(n)+a^(n) for any odd positive integer n .