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If-a-seller-could-purchase-goods-at-an-8-lower-price-by-keeping-the-selling-price-fixed-his-profit-over-the-cost-price-would-increase-from-the-current-x-to-x-10-So-what-is-the-value-of-x-

Question Number 71439 by Mr. K last updated on 15/Oct/19 $${If}\:{a}\:{seller}\:{could}\:{purchase}\:{goods}\:{at}\:{an} \\ $$$$\mathrm{8\%}\:{lower}\:{price}\:{by}\:{keeping}\:{the}\:{selling} \\ $$$${price}\:{fixed},\:{his}\:{profit}\:{over}\:{the}\:{cost} \\ $$$${price}\:{would}\:{increase}\:{from}\:{the}\: \\ $$$${current}\:{x\%}\:{to}\:\left({x}+\mathrm{10}\right)\%.\:{So},\:{what}\:{is} \\ $$$${the}\:{value}\:{of}\:{x}? \\ $$ Commented by…

Prove-that-log-n-gt-3n-10-1-2-1-3-1-4-1-n-1-

Question Number 5900 by 314159 last updated on 04/Jun/16 $${Prove}\:{that} \\ $$$${log}\:{n}!\:>\frac{\mathrm{3}{n}}{\mathrm{10}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right). \\ $$ Answered by Yozzii last updated on 05/Jun/16 $${Let}\:{for}\:{n}\in\mathbb{N},{n}\geqslant\mathrm{2},\: \\ $$$${P}\left({n}\right):\:{logn}!>\frac{\mathrm{3}{n}}{\mathrm{10}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right). \\…