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(5.3.5) How to Prove Inequalities with Mathematical Induction for Positive Integers This video covers the proof of an inequality involving powers of 2 and factorials using mathematical induction for positive integers. We focus on the proposition P(n) which states that 2 raised to the power of n is less than n plus 1 factorial for every positive integer n. We start by checking the validity of P(2) by plugging in 2 for n, which gives us 2 squared is less than 2 plus 1 factorial. This simplifies to
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