Question Number 21573 by Tinkutara last updated on 27/Sep/17
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{1}\:<\:\frac{\mathrm{1}}{\mathrm{1001}}\:+\:\frac{\mathrm{1}}{\mathrm{1002}}\:+\:\frac{\mathrm{1}}{\mathrm{1003}}\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{3001}}\:<\:\mathrm{1}\frac{\mathrm{1}}{\mathrm{3}}. \\ $$