How Induction Works: Base Case, Hypothesis and Step Worksheet with Answer Key

What's on the worksheet

1. For each claim, write the base case P(n_0) at the first value of n the claim is about, and show that it is true.
   \sum_{i=1}^{n} (4i - 1) = n(2n + 1), for n \ge 14 divides 3^{2n-1} + 1, for n \ge 1n^2 \ge 3n + 4, for n \ge 4\sum_{i=0}^{n} 3 \cdot 4^i = 4^{n+1} - 1, for n \ge 0
2. Let $P
4. A sequence is defined by a_1 = 1 and a_n+1 = a_n1 + a_n for n ≥ 1.
5. Consider the claim 2^n > 2n + 1.
6. A classmate wants to prove _i=1^n 12^i = 1 - 12^n for every n ≥ 1 and writes this as the whole proof.