Answer: [n(n + 1)/2]².
- A [n(n + 1)/2]²
- B n(n + 1)/2
- C n²
- D n(n + 1)(2n + 1)/6
Correct answer: A. [n(n + 1)/2]²
Explanation: The sum of the first n cubes is the square of the sum of the first n numbers.
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.