Question Number 2642 by Rasheed Soomro last updated on 24/Nov/15 $${n}\:{lines}\:{are}\:{drawn}\:{inside}\:{a}\:{circle}\:{in}\:{such}\:{a}\:{way}\:{that}\: \\ $$$${the}\:{circle}\:{has}\:{been}\:{divided}\:{in}\:{maximum}\:{number}\:{of} \\ $$$${parts}.\:{Determine}\:{this}\:{maximum}\:{number}. \\ $$ Commented by RasheedAhmad last updated on 24/Nov/15 $$\bullet{One}\:{line}\:{can}\:{divide}\:{the}\:{circle}…
Question Number 133708 by Dwaipayan Shikari last updated on 23/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\left(\pi+{e}\right){n}\right)}{{n}^{\mathrm{4}} } \\ $$ Answered by mindispower last updated on 24/Feb/21 $$\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{{sin}\left({nx}\right)}{{n}}={Im}\:\underset{{n}\geqslant\mathrm{1}}…
Question Number 68171 by naka3546 last updated on 06/Sep/19 Commented by mathmax by abdo last updated on 06/Sep/19 $$ \\ $$$$\sqrt{\mathrm{5}−\mathrm{2}\sqrt{{x}}\:}\:{is}\:{not}\:{defined}\:{on}\:+\infty\:! \\ $$ Commented by…
Question Number 2629 by Filup last updated on 24/Nov/15 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{evalate}: \\ $$$${A}=\int_{{a}} ^{\:{b}} \lfloor{f}\left({x}\right)\rfloor{dx} \\ $$$$ \\ $$$${for}\:{example}: \\ $$$$\int_{\mathrm{0}.\mathrm{5}} ^{\:\mathrm{2}.\mathrm{5}} \lfloor{x}^{\mathrm{2}} \rfloor{dx} \\ $$…
Question Number 133696 by Mikael_786 last updated on 23/Feb/21 $$\mathrm{A}\:\mathrm{test}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{four}\:\mathrm{questions} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{contains}\:\mathrm{five}\:\mathrm{alternative} \\ $$$$\mathrm{answers},\:\mathrm{one}\:\mathrm{of}\:\mathrm{which}\:\mathrm{is}\:\mathrm{correct}. \\ $$$$\mathrm{The}\:\mathrm{test}\:\mathrm{pass}\:\mathrm{condition}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{four}\:\mathrm{correct}\:\mathrm{answers}.\:\mathrm{A}\:\mathrm{student},\:\mathrm{not} \\ $$$$\mathrm{knowing}\:\mathrm{the}\:\mathrm{test}\:\mathrm{subject},\:\mathrm{scored}\:\mathrm{the} \\ $$$$\mathrm{answers}\:\mathrm{randomly}.\mathrm{How}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{for}\:\mathrm{the}\:\mathrm{student}\:\mathrm{to}\:\mathrm{pass}? \\…
Question Number 68161 by Learner-123 last updated on 06/Sep/19 $${In}\:{my}\:{textbook}\:{its}\:{written}: \\ $$$${In}\:{applying}\:{the}\:{nth}−{term}\:{test}\:{we}\: \\ $$$${can}\:{see}\:{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \:{diverges}\:{because}\: \\ $$$${lim}_{{n}\rightarrow\infty} \left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \:{does}\:{not}\:{exist}. \\ $$$${But}\:{then}\:{why}\:\underset{{n}=\mathrm{1}}…
Question Number 2624 by prakash jain last updated on 23/Nov/15 $$\mathrm{Old}\:\mathrm{question}\:\mathrm{related}\:\mathrm{to}\:\mathrm{greatest}\:\mathrm{int}\:\mathrm{function}. \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\lfloor\mathrm{1}+{x}\rfloor=\mathrm{1} \\ $$$$\lfloor\mathrm{1}\rfloor=\mathrm{1} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\lfloor\mathrm{1}−{x}\rfloor=? \\ $$ Answered by Filup last…
Question Number 133692 by Dwaipayan Shikari last updated on 23/Feb/21 $$\frac{{sin}\mathrm{1}}{{e}}−\frac{{sin}\left(\mathrm{2}\right)}{\mathrm{2}{e}^{\mathrm{2}} }+\frac{{sin}\left(\mathrm{3}\right)}{\mathrm{3}{e}^{\mathrm{3}} }−\frac{{sin}\left(\mathrm{4}\right)}{\mathrm{4}{e}^{\mathrm{4}} }+…={tan}^{−\mathrm{1}} \left(\frac{{sin}\left(\mathrm{1}\right)}{{cos}\left(\mathrm{1}\right)+{e}}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 23/Feb/21…
Question Number 2621 by Yozzi last updated on 23/Nov/15 $${If}\:{you}\:{have}\:{n}\:{non}−{parallel} \\ $$$${lines}\:{in}\:{a}\:{plane},\:{how}\:{many}\:{points} \\ $$$${of}\:{intersection}\:{are}\:{there}? \\ $$ Answered by prakash jain last updated on 23/Nov/15 $$\mathrm{Choose}\:\mathrm{any}\:\mathrm{2}\:\mathrm{lines}\:\mathrm{and}\:\mathrm{we}\:\mathrm{get}\:\mathrm{point}\:\mathrm{of}…
Question Number 2619 by Rasheed Soomro last updated on 23/Nov/15 $${The}\:{sums}\:{of}\:{the}\:{first}\:\:{n}\:\:\:{terms}\:{of}\:{two}\:{AP}\:'{s}\:{are} \\ $$$${in}\:{the}\:{ratio}\:\:\mathrm{3}{n}+\mathrm{31}\::\:\:\mathrm{5}{n}−\mathrm{3}\:.\:{Show}\:{that}\:{their}\:\mathrm{9}^{{th}} \:{terms} \\ $$$${are}\:{equal}. \\ $$ Commented by Yozzi last updated on 24/Nov/15…