Answer: the statement is not proven.
- A the statement is not proven
- B the statement is proven
- C it holds for k only
- D it holds for all n
Correct answer: A. the statement is not proven
Explanation: Without a valid base case the inductive chain never starts, so nothing is actually proved.
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.