Answer: (n + 1)! − 1.
- A n!
- B (n + 1)! − 1
- C (n + 1)!
- D n!·n
Correct answer: B. (n + 1)! − 1
Explanation: Since k·k! = (k+1)! − k!, the sum telescopes to (n + 1)! − 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.