When proving an inequality of the form $P(n) \implies P(n+1)$ using mathematical induction, what is the most critical step to ensure the inductive step holds?
Question 2
Consider the statement: 'For all integers $n \ge 2$, $n! > 2^n$'. Which of the following is the correct base case for a proof by induction?
Question 3
To prove that the equation $x^2 + 1 = 0$ has no real solutions, which proof technique is most appropriate?
Question 4
Which of the following statements about constructive proofs is true?
Question 5
When proving an inequality using mathematical induction, if the inductive hypothesis is $P(k): k^2 > 2k+1$ for some integer $k \ge 3$, what is the goal for the inductive step $P(k+1)$?
Advanced Proof Quiz — A-Level Further Mathematics | A-Warded
