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Question-144291

Question Number 144291 by SOMEDAVONG last updated on 24/Jun/21 Answered by som(math1967) last updated on 24/Jun/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{2021}} \frac{\left(\mathrm{2021}−{x}\right)^{\mathrm{2021}} }{\left(\mathrm{2021}−{x}\right)^{\mathrm{2021}} +\left(\mathrm{2021}−\mathrm{2021}+{x}\right)^{\mathrm{2021}} }{dx} \\ $$$$\mathrm{2}{I}=\int_{\mathrm{0}} ^{\mathrm{2021}}…

S-n-n-1-n-1-2-k-tanh-1-2-k-

Question Number 144272 by SOMEDAVONG last updated on 24/Jun/21 $$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{k}} }\mathrm{tanh}\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{k}} }\right)=? \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jun/21 $$\mathrm{S}_{{n}}…

Find-the-value-of-lim-n-k-n-2n-1-k-k-

Question Number 144261 by ZiYangLee last updated on 23/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}={n}} {\overset{\mathrm{2}{n}} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}. \\ $$ Commented by Dwaipayan Shikari last updated on 23/Jun/21 $$\underset{{n}\rightarrow\infty}…

Find-the-sum-of-all-the-real-number-x-that-satisfy-2x-2-5x-1-2x-3-1-

Question Number 144260 by ZiYangLee last updated on 23/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{number} \\ $$$${x}\:\mathrm{that}\:\mathrm{satisfy}\:\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}\right)^{\mathrm{2}{x}−\mathrm{3}} =\mathrm{1} \\ $$ Answered by Ar Brandon last updated on 24/Jun/21 $$\mathrm{2x}−\mathrm{3}=\mathrm{0}\:\vee\:\mathrm{2x}^{\mathrm{2}}…