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.

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

if A={:[(1,1,1),(1,1,1),(1,1,1)]:}, prove by mathematical induction that, A^(n)={:[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]:} for every positive integer n.

By the principle of mathematical induction prove that 1+2+3+4+…n= (n(n+1))/2

Prove by mathematical induction 1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)

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

Let A=({:(1,1,1),(0,1,1),(0,0,1):}) . Then for positive integer n, A^n is

If p be a natural number, then prove that, p^(n+1)+(p+1)^(2n-1) is divisible by (p^(2)+p+1) for every positive integer n.

Prove by mathematical induction that (11^(n+2)+12^(2n+1)) is divisible by 133 for all non-negative integers.

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)