Prove $5^n + 3^n - 2^{2n+1} > 0$ by induction I am not sure how to deal with the $-2^{2n+1}$ term.
I did the basis proof for n=1
I am stuck at this step:
$$
5^{k+1}+3^{k+1}-2^{2(k+1)+1} = 5\cdot 5^k + 3 \cdot 3^k -2^3 \cdot 2^{2k}
$$
Any advice guys?

The base case is simple.
We now assume $5^k+3^k-2^{2k+1}>0$. Then multiplying by 4 yields $4\cdot 5^k + 4 \cdot 3^k - 4\cdot 2^{2k+1}>0$, which implies $5\cdot 5^k + 3\cdot 3^k -2^{2k+3} > 5^k - 3^k >0$ as required.
