Prove
if $d(n)$ is $O(f(n))$ and $e(n)$ is $O(g(n))$, then $d(n) + e(n)$ is $O((f(n) + g(n)))$.
What I tried.
if $d(n)$ is $O(f(n))$ then $d(n) \leq c_1 \cdot f(n)$ if $e(n)$ is $O(g(n))$ then $e(n) \leq c_2 \cdot f(n)$
which implies $d(n) + e(n) \leq c_1\cdot f(n) + c_2\cdot g(n)$.
I am unable to proceed further than this. Please help.