[Solved]: Finding big O notation of function with two parameters

Some of modifications of O described in Concrete Mathematics: Foundation for Computer Science says: $ qquad O(f(n)) + O(g(n)) = O(mid f(n)mid + mid g(n) mid) qquad (9.22) qquad O(f(n))O(g(n)) = O(f(n)g(n)) qquad qquad qquad (9.26) $ And using some basic knowledge of O notation and functions: $ qquad O(f(n) +c) = O(f(n)) qquad forall_{nin mathbf N} forall_{k>0} n^k > 0 $ Use those transformation you can came up with something like this: $$frac{n^{s+1}-1}{n-1}-1 = Oleft(frac{n^{s+1}-1}{n-1}-1right) = Oleft(frac{n^{s+1}-1}{n-1}right) = Oleft(frac{1}{n-1}right)Oleft(n^{s+1}-1right) = $$ $$ Oleft(frac{1}{n}right)Oleft(n^{s+1}right) = Oleft(frac{n^{s+1}}{n}right) = O(n^s) $$ So your intuition was right.