Answer: 1 + 4 = 2(3)(5)/6.
- A 1 + 4 = 2(3)(5)/6
- B 1 + 4 = 10
- C 5 = 5
- D 1 + 2 = 5
Correct answer: A. 1 + 4 = 2(3)(5)/6
Explanation: P(2) states 1<sup>2</sup> + 2<sup>2</sup> = 2(3)(5)/6. Left side = 1+4 = 5, right side = 30/6 = 5. Both equal 5, confirming P(2) is true.
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.