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Question-218658

Question Number 218658 by Nicholas666 last updated on 14/Apr/25 Answered by Nicholas666 last updated on 14/Apr/25 Commented by A5T last updated on 14/Apr/25 $$\mathrm{x}\leqslant\mathrm{3}\:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{1}\:\mathrm{does}\:\mathrm{not}\:\mathrm{imply}\:\mathrm{xy}\leqslant\mathrm{3} \\…

Question-218651

Question Number 218651 by hardmath last updated on 13/Apr/25 Answered by vnm last updated on 14/Apr/25 $$=\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}−\mathrm{4}\centerdot\frac{\mathrm{1}}{\mathrm{4}}\right)+ \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{8}}−\mathrm{4}\centerdot\frac{\mathrm{1}}{\mathrm{8}}\right)+ \\ $$$$…+ \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{4}{n}−\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}{n}−\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}{n}−\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{4}{n}}−\mathrm{4}\centerdot\frac{\mathrm{1}}{\mathrm{4}{n}}\right)= \\ $$$$\underset{{k}=\mathrm{1}}…