Answer: the (k + 1)th term.
- A the (k + 1)th term
- B the very first term
- C the number zero
- D the value n
Correct answer: A. the (k + 1)th term
Explanation: Adding the (k + 1)th term to P(k) lets us derive P(k + 1).
Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.
Concept context
A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.