<s>[INST] 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?
 [/INST] $5(5^k)+3(3^k)-2^3(2^{2k})=3(5^k+3^k-2^{2k+1})+2(5^k)-2(2^{2k})>3(0)+2(5^5-4^k)>0$
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