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Advanced Inequalities

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Explanations 1

See Scott Aaronson's nice blog post "How to upper-bound the probability of something bad" for his personal list of techniques.
By Victor Wang

Problems 1

If A,B,CA,B,CA,B,C are positive reals such that An≥BnCA^n \ge \frac{B^n}{C}An≥CBn for n=1,2,3,…n=1,2,3,\dotsn=1,2,3,…, then what can we conclude?