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Problem 366

AMC 12 late, AIME early

Algebra Difficulty 4.7 Find the answer

5. Let $P=\frac{2^{2019}+1}{2^{2020}+1}, Q=\frac{2^{2020}+1}{2^{2021}+1}$ , then the relationship between $P$ and $Q$ is ( ).
A. $P>Q$
B. $P<Q$
C. $P=Q$
D. Cannot be determined

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

Answer: A

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.