What is an easy way for finding C and N when proving the Big-Oh of an Algorithm?

Question

I\'m starting to learn about Big-Oh notation.

What is an easy way for finding C and N₀ for a given function?

Say, for example:

(n+1)⁵

Answer 1

Usually the proof is done without picking concrete C and N₀. Instead of proving f(n) < C * g(n) you prove that f(n) / g(n) < C.

For example, to prove n³ + n is O(n³) you do the following:

(n³ + n) / n³ = 1 + (n / n³) = 1 + (1 / n²) < 2 for any n >= 1. Here you can pick any C >= 2 with N₀ = 1.