Answer: 2ⁿ − 1.
- A 2ⁿ − 1
- B just 2ⁿ
- C n² only
- D only 2n
Correct answer: A. 2ⁿ − 1
Explanation: This geometric series of n terms sums to 2ⁿ − 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.