21. [-/5 Points] DETAILS HUNTERDM3 3.2.003. MY NOTES ASK YOUR TEACHER Consider the following recurrence relation. B(n) = if n = 1 (3 . B(n - 1 ) + 2 ifn > 1 Use induction to prove that B(n) = 37 - 1. (Induction on n.) Let f(n) = 37 - 1. Base Case: If n = 1, the recurrence relation says that B(1) = 2, and the formula says that f(1) = 3 - 1 = so they match. Inductive Hypothesis: Suppose as inductive hypothesis that B(k - 1) = for some k > 1. Inductive Step: Using the recurrence relation, B(k) = 3 . B(k - 1) + 2, by the second part of the recurrence relation = + 2, by inductive hypothesis = (3* - 3) + 2 so, by induction, B(n) = f(n) for all n 2 1. eBook