Prove $$\int_0^{\pi}\left|{\sin nx\over x}\right|\,dx\ge\frac2\pi\left(1+\frac12+\frac13\dots+\frac1n\right)$$ I'm not sure how to start. Any help will be appreciated. Thank you
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You have already asked exactly the same question. – Jack D'Aurizio Apr 29 '18 at 17:32