How to prove that this function is primitive recursive?

[Discrete Mathematics] How to prove a function is big-theta(n^3/2)?

• The function I was given is (n+1)3/2. I understand that I have to prove that it is both big-O(n3/2) and big-Omega(n3/2). I know how to do this for polynomial functions such as n2 and ...show more

• Answer:

  Upper bound. For all n > 1: (n+1)^(3/2) < (n+n)^(3/2) = 2^(3/2) * n^(3/2). Lower bound. For all n > 0: (n+1)^(3/2) > (n+0)^(3/2) = n^(3/2). All together, we have 1 * n^(3/2) < (n+1)^(3/2) < 2^(3/2) * n^(3/2) for all n > 1. Hence, (n+1)^(3/2) is Θ(n^(3/2)). I hope this helps!