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 using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+3)le(n+3)!

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=(1)/(2)n(3n+1)

If A,=[[3,-41,1]], then prove that A^(n),=[[1+2n,-4n][2n], where n is any positive integer.

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.

Prove the following by the principle of mathematical induction: 1+3+3^(2)++3^(n-1)=(3^(n)-1)/(2)

Prove the following by the principle of mathematical induction: 1.2+2.3+3.4++n(n+1)=(n(n+1)(n+2))/(3)

Prove the following by using the Principle of mathematical induction AA n in N 2^(3n-1) is divisble by 7.

Prove the following by the principle of mathematical induction: 5^(n)-1 is divisible by 24 for all n in N.