Question Number 115429 by Eric002 last updated on 25/Sep/20 $${how}\:{many}\:{ways}\:{can}\:{you}\:{arrange}\:\mathrm{15}\:{distinct} \\ $$$${balls}\:{into}\:\mathrm{5}\:{cups}\:{if}\:{there}\:{has}\:{to}\:{be}\:{at}\:{least} \\ $$$$\mathrm{1}\:{ball}\:{in}\:{each}\:{cup}? \\ $$$$ \\ $$ Commented by bemath last updated on 26/Sep/20…
Question Number 115417 by toa last updated on 25/Sep/20 $$\mathrm{with}\:\mathrm{the}\:\mathrm{use}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{n}!>\mathrm{2n}^{\mathrm{3}} ,\:\forall\mathrm{n}\geqslant\mathrm{6}. \\ $$ Answered by TANMAY PANACEA last updated on 25/Sep/20 $${when}\:{n}=\mathrm{6} \\…
Question Number 115405 by mathdave last updated on 25/Sep/20 $${find}\:{the}\:{close}\:{form}\:{of} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 115401 by Khalmohmmad last updated on 25/Sep/20 $$\int\frac{\sqrt{\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}=? \\ $$ Answered by Dwaipayan Shikari last updated on 25/Sep/20 $$\mathrm{2}\int\frac{\mathrm{t}^{\mathrm{2}} }{\mathrm{t}^{\mathrm{4}} +\mathrm{1}}\mathrm{dt}=\int\frac{\mathrm{1}}{\left(\mathrm{t}^{\mathrm{2}} −\mathrm{i}\right)}+\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{2}}…
Question Number 115396 by Sudip last updated on 25/Sep/20 $$\mathrm{If}\:\mathrm{a}\:\mathrm{page}\:\mathrm{is}\:\mathrm{torn}\:\mathrm{from}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{book},\:\mathrm{then} \\ $$$$\mathrm{the}\:\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{pages}\:\mathrm{is}\:\mathrm{718797}\:\mathrm{so} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{torn}\:\mathrm{pages}? \\ $$ Answered by PRITHWISH SEN 2 last updated on 25/Sep/20…
Question Number 180935 by SANOGO last updated on 19/Nov/22 $$\int_{} \frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Answered by Frix last updated on 19/Nov/22 $$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}+\int\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{1}}=…
Question Number 49859 by hassentimol last updated on 11/Dec/18 Commented by hassentimol last updated on 11/Dec/18 $$\mathrm{Could}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{why}\:\mathrm{this}\:? \\ $$$$\mathrm{I}\:\mathrm{know}\:\mathrm{that}\:\mathrm{0}.\mathrm{999}…=\mathrm{1}\:\mathrm{is}\:\mathrm{true}\:\mathrm{but}\:\mathrm{why}\:\mathrm{the} \\ $$$$\mathrm{above}\:\mathrm{shown}\:\mathrm{is}\:\mathrm{correct}\:?\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{undersand}\:\mathrm{it}… \\ $$ Commented by…
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Question Number 115391 by Faetma last updated on 25/Sep/20 $$\mathrm{Who}\:\mathrm{can}\:\mathrm{explain} \\ $$$$\mathrm{me}\:\mathrm{what}\:\mathrm{is}\:“\mathbb{R}_{{n}} \left[{x}\right]''? \\ $$$${In}\:{French}\:{if}\:{possible}. \\ $$ Answered by Olaf last updated on 26/Sep/20 $$\mathrm{Le}\:\mathbb{R}\:\mathrm{c}'\mathrm{est}\:\mathrm{l}'\mathrm{ensemble}\:\mathrm{des}\:\mathrm{reels}.…
Question Number 115384 by mathdave last updated on 25/Sep/20 $${solve}\:{the}\:{limit}\:{problem} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{cos}{x}}{\mathrm{1}−{e}^{−{x}} }\right) \\ $$ Answered by MJS_new last updated on 25/Sep/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}−\mathrm{e}^{−{x}}…