Answer: (k + 1)(k + 2)/2.
- A (k + 1)(k + 2)/2
- B only (k + 1)/2
- C only k(k + 1)/2
- D only (k + 2)/2
Correct answer: A. (k + 1)(k + 2)/2
Explanation: k(k+1)/2 + (k+1) = (k+1)(k+2)/2, which is the formula with n = 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.