Answer: n(n + 1).
- A n(n + 1)
- B n²
- C 2n
- D n(n + 1)/2
Correct answer: A. n(n + 1)
Explanation: 2 + 4 + … + 2n = 2(1 + 2 + … + n) = 2·n(n+1)/2 = n(n + 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.