Proof by Induction

What is the first step in a proof by mathematical induction?

In the induction step, if the statement is true for n = k, what must be shown next?

Which of the following is a correct induction hypothesis for proving the formula for the sum of first n natural numbers?

Using induction, prove that 2^n > n^2 for all integers n ≥ 5. What is the base case?

For the statement P(n): 1^3 + 2^3 + ... + n^3 = (n(n + 1)/2)^2, what is the induction step?

Which of the following sums can be proved by induction?

Prove by induction that for all n ≥ 1, 3^n ≥ 2n + 1. What is the inductive hypothesis?

Using induction, prove that n! > 2^n for all integers n ≥ 4. What is the key inequality used in the induction step?

Which of the following is NOT a valid use of mathematical induction?

Prove by induction that for n ≥ 1, 7 divides 8^n - 1. What is the base case?