Hello everyone. I've been looking at examples and I can't seem to see what they are doing. For example, the book has: Suppose that d1, d2, d3 ... is a sequence defined as follows: d1 = 9/10, d2 = 10/11. dk = dk-1 * dk-2 for all inegers k >= 3. Prove that dn =< 1 for all integers n >= 0. The book says: Proof (by strong mathematical induction): let the property P(n) be the inequality dn =< 1. Show that the proeprty is true for n = 1, and n =2: I understand why they are starting at n = 1, but why are they testing 2 cases? If i had say, d1 = 9/10, d2 = 10/11, d3 = 10/12, then would i have to test for n = 1, n = 2, and n = 3? They then go onto say, Show that for any integer k > 2, if the property is true for all integeers i with 1 =< i < k, then it is true for k: I'm confused on how they are getting k > 2, also how did they figure out that range from 1 = < i < k ? My problem looks very similar to this one, but it has 3 subscripts instead of one: I would think k >= 3, becuase thats the problem states, that ek = ek -1, ek-2, ek-3 for all integers k >= 3 THanks!