If `A=[1 1 1 0 1 1 0 0 1]` , then use the principle of mathematical induction to show that `A^n=[1nn(n+1)//2 0 1n0 0 1]` for every positive integer `n` .

If A=[1 1 1 0 1 1 0 0 1] , then use the principle of mathematical induction to show that A^n=[1 n n(n+1)//2 0 1 n 0 0 1] for every positive integer n .

If A=[111011001] ,then use the principle of mathematical induction to show that A^(n)=[1nn(n+1)/201n001] for every positive integer n.

Using the principle of mathematical induction to show that tan^(-1)(n+1)x-tan^(-1)x , forall x in N .

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: If A=[a1 0a] , then A^n=[a^nn a^(n-1)0a^n] for every positive integer ndot

If a is a non-zero real or complex number.Use the principle of mathematical induction to prove that: If A=[a10a], then A^(n)=[a^(n)a^(n-1)0a^(n)] for every positive integer n .

1/(n+1) + 1/(n+2)+…..+ 1/(3n+1) gt 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 is a non-zero real or complex number. Use the principle of mathematical induction to prove that: IfA=[[a,1],[ 0,a]],t h e nA^n=[[a^n,n a^(n-1)],[0,a^n]] for every positive integer n.

Prove the following by principle of mathematical induction If A=[[3,-4] , [1,-1]] , then A^n=[[1+2n, -4n] , [n, 1-2n]] for every positive integer n

Prove the following by principle of mathematical induction If A=[[3,-4] , [1,-1]] , then A^n=[[1+2n, -4n] , [n, 1-2n]] for every positive integer n