Prove by method of induction: `P(n) = [[3,-4],[1,-1]]^n = [[2n+1, -4n],[n, -2n+1]]`

Prove the following by the method of induction for all n in N : Prove by methode of Induction [[1,2],[0,1]]^n = [[1,2n],[0,1]] AA n in N

Answer the following questions.If A=[[3,-4],[1,-1]] ,prove that A^n=[[1+2n,-4n],[n,1-2n]] for all n in N

Prove by method of induction: log_(a)x^(n) = n log_(a) x, x gt 0, n in N

Prove by method of induction 15^(2n-1) + 1 is divisible by 16, for all n in N

Prove by method of induction: 5^(2n)-2^(2n) is divisible by 3, for all n in N .

Prove by Method of Induction n^2 < 2^n , AA n in N and n ge 5

If (1-i)^n = 2^n , then n=

Prove, by method of induction, for all n in N : 1^2 + 4^2 + 7^2 +...+ (3n - 2)^2 = n/2 (6n^2 - 3n - 1)

Prove by Method of Induction n^3 - 7n + 3 is divisible by 3, AA n in N

Prove, by method of induction, for all n in N : 2 + 3.2 +4.2^2 +...+ (n + 1) (2^(n-1)) = n.2^n