1. The problem statement, all variables and given/known data Give a big-O estimate of the product of the first n odd positive integers. 2. Relevant equations Big-O notation: f(x) is O(g(x)) if there are constants C and k such that |f(x)| ≤ C|g(x)| whenever x > k. 3. The attempt at a solution The product of the first n odd integers can be given by: [tex]P(n)=1\times 3\times 5\times 7\times...\times (2n-1)[/tex] For n > 0, no element in the above sequence will be greater than (2n-1). Thus: [tex]1\times 3\times 5\times 7\times...\times (2n-1)\leq (2n-1)\times (2n-1)...\times (2n-1)=(2n-1)^n[/tex] So: P(n) ≤ (2n-1)n whenever n > 0 I could stop here and say that P(n) is O((2n-1)n) But to simplify I think I could consider that: P(n) ≤ (2n-1)n ≤ (2n)n Thus, P(n) is O((2n)n) Is this reasoning correct? Thank you in advance.