Answer: k+1.
- A n
- B k+1
- C k
- D 2k+1
Correct answer: B. k+1
Explanation: Assuming 1+2+...+k = k(k+1)/2, we add the next term (k+1) to both sides to extend the sum to 1+2+...+k+(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.