Asymptotic relationship demonstration I have to demonstrate that if
$$
\begin{split}
f_1(n) &= \Theta(g_1(n)) \\
f_2(n) &= \Theta(g_2(n)) \\
\end{split}
$$
then
$$
f_1(n) + f_2(n) = \Theta(\max\{g_1(n),g_2(n)\})
$$
Actually I have already proved that $$f_1(n)+f_2(n) = O(\max\{g_1(n),g_2(n)\}).$$
My problem is $$f_1(n)+f_2(n) = \Omega(\max\{g_1(n),g_2(n)\}),$$ could you help me?

$f_1(n)=\mathbf{\theta}(g_1(n)) \Rightarrow \forall n>N_1;c_1f_1(n)\geq g_1(n)$
$f_2(n)=\mathbf{\theta}(g_2(n)) \Rightarrow \forall n>N_2;c_2f_2(n)\geq g_2(n)$
so
$\forall n>max\{N_1,N_2\};max\{c_1,c_2\}(f_1(n)+f_2(n))\geq 2 max\{g_1(n),g_2(n)\}$
