If `A={:[(1,2),(0,1)]:}` show, by mathematical induction, that `A^(n)={:[(1,2n),(0,1)]:}` for all `n in N.`

If A={:[(3,-4),(1,-1)]:}, then by principle of mathematics induction show that, A^(n)={:[(1+2n,-4n),(n,1-2n)]:} for all n in N.

If A={:[(1,1,1),(0,1,1),(0,0,1)] , Prove by mathematical induction that, A^(n)={:[(1,n,(n(n+1))/2),(0,1,n),(0,0,1)] for every positive integer n.

If A={:[(a,b),(0,1)]:}, prove by mathematical induction that, A^(n)= [{:(,a^(n), (b(a^(n) -1))/(a-1)),(,0,1)]:} for every positive integer n.

Using mathematical induction to show that p^(n+1) +(p+1)^(2n-1) is divisible by p^2+p+1 for all n in N

Using mathematical induction prove that (d)/(dx)(x^n)= nx^(n-1) for all positive integers n.

Prove by mathematical induction , 3^(2n+1)+2^(n+2) is divisible by 7, n in N

Prove by mathematical induction that 1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n+1)) = n/(2n+1),(n in N)

Prove by induction that n(n+1)(2n+1) is divisible by 6 for all ninNN .

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

If n in N,then prove by mathematical induction that 7^(2n)+2^3(n-1).3^(n-1) is always a multipe of 25.