Sea $f: R^+ \to R$ defined as $$f (x) = \frac{1}{\sqrt[3]{x^2 + 6x + 9} + \sqrt[3]{x^2 + 4x + 3} + \sqrt[3]{x^2 + 2x + 1}}$$Calculate $$f (1) + f (2) + f (3) + ... + f (2016).$$
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist F2 day2 (F= Functions)
Tags: algebra, Sum, radical