Simple induction proof that $3^n + 5^n \ge 2^{n+2}$ Im having a lot of trouble proving by induction that $3^n + 5^n \geq 2^{n+2}.$
The base step is easy, but I don't seem to find the way to proof the inductive step.

Inductive step
$$3^{n+1} + 5^{n+1}=3\times3^{n} + 5\times5^{n}\geq2(3^{n} + 5^{n}) \geq2\times 2^{n+2}=2^{n+3}$$
