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

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

Prove by Method of Induction 4^n - 1 is divisible by 3, for each number n

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

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

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

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

Prove by the method of Induction for all n in N : 1/3.5 + 1/5.7 + 1/7.9 + …. n terms = n/(3(2n+3))

Prove, by method of induction, for all n in N : 2 + 3.2 +4.2^2 +...+ (n + 1) (2^(n-1)) = n.2^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, for all n in N : 8 + 17 + 26 +...+ (9n - 1) = n/2 (9n + 7)