If `A=[a b0 1]` , prove that `A^n=[a^n b((a^n-1)/(a-1))0 1]` for every positive integer `n` .

If A=[ab01], prove that A^(n)=[a^(n)b((a^(n)-1)/(a-1))01] for every positive integer n.

If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] for every positive integer n .

If A=[[a,b],[0,1]] then prove that A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]

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 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 .

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.

If a is a non-zero real or complex number.Use the principle of mathematical induction to prove that: If A=[[a,10,a]],then A^(n)=[[a^(n),na^(n-1)0,a^(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] , 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 .