Answer: n/(n + 1).
- A 1/(n + 1)
- B n/(n + 1)
- C (n − 1)/n
- D n/(2n + 1)
Correct answer: B. n/(n + 1)
Explanation: The telescoping sum equals 1 − 1/(n + 1) = 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.