Salad & Dressing & Mathematics

South Korea's first year of middle school math problem.

Problem) Domain and codomain of the entire set of two natural function f(x) by f(x) = 1, f(a+b) = f(a) + f(b) + ab and when satisfied, The value of f(1) + f(2) + f(3) ++ f(10) ?

This problem is a function of salad dressing, topped with a sequence problem.