Christopher Stone

2022-04-09

How to prove the inequality

$\frac{1}{n}+\frac{1}{n+1}+\cdots +\frac{1}{2n-1}\ge \mathrm{log}\left(2\right)?$

mislifola5vo

Beginner2022-04-10Added 11 answers

Use Riemann sum. Observe

$\frac{1}{n}+\cdots +\frac{1}{2n-1}\ge {\int}_{n}^{2n}\frac{1}{x}dx=\mathrm{log}2n-\mathrm{log}n=\mathrm{log}2.$

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