Math Is Fun Forum

If I assume that f1(n) is O(g1(n)) and f2(n) is O(g2(n)) prove

f1(n) + f2(n) is O(max(g1(n), g2(n)))

Here is what I have so far:

f1(n) <= c1*g1(n) for n >= N1
f2(n) <= c2*g2(n) for n >= N2

so f1(n) + f2(n) <= (c1*g1(n)) + (c2 * g2(n)) for n >= max(N1, N2)

it is from here to the finish that I am lost on where to go next. 

I apologize if this is a poor question but I would appreciate any help provided.