Question Number 209911 by 073 last updated on 25/Jul/24 Commented by mr W last updated on 25/Jul/24 $${what}'{s}\:{the}\:{difference}\:{between} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right)^{\mathrm{2}} \:{and}\:\left(\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right)^{\mathrm{2}} \right)? \\ $$ Commented…
Question Number 209881 by naka3546 last updated on 24/Jul/24 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{satisfies} \\ $$$$ \\ $$$${a}_{{n}} \:=\:\mathrm{1}\:+\:\sqrt{\frac{\mathrm{1}}{{n}}}\:−\:\sqrt{\frac{\mathrm{1}}{{n}+\mathrm{1}}}\:−\:\sqrt{\frac{\mathrm{1}}{{n}}\:−\:\frac{\mathrm{1}}{{n}+\mathrm{1}}} \\ $$$$ \\ $$$$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{value}\:\:\mathrm{of}\: \\ $$$$ \\ $$$$\:\:\:{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}}…
Question Number 209883 by Ismoiljon_008 last updated on 24/Jul/24 Commented by Ismoiljon_008 last updated on 24/Jul/24 $$\:\:\:{help}\:,\:{please} \\ $$ Commented by Frix last updated on…
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Question Number 209783 by Ismoiljon_008 last updated on 21/Jul/24 Answered by mr W last updated on 21/Jul/24 Commented by mr W last updated on 21/Jul/24…
Question Number 209794 by Ismoiljon_008 last updated on 21/Jul/24 $$\:\:\: \\ $$$$\:\:\:\mathrm{13456622577532674}\:{how}\:{many}\:\mathrm{5}-{digit} \\ $$$$\:\:\:{numbers}\:{can}\:{be}\:{made}\:{from}\:{these}\:{numbers}? \\ $$$$\:\:\:{help}\:{please} \\ $$$$ \\ $$ Answered by MM42 last updated…
Question Number 209761 by pablo1234523 last updated on 20/Jul/24 $${x}^{\mathrm{3}} −\mathrm{9}{xy}^{\mathrm{2}} =\mathrm{28} \\ $$$${x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{15} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y}. \\ $$$${x},{y}\in\mathbb{R} \\ $$ Answered by mr…
Question Number 209763 by Ismoiljon_008 last updated on 20/Jul/24 Commented by Ismoiljon_008 last updated on 20/Jul/24 $$\:\:\:\mathscr{F}{ind}\:{the}\:{number}\:{of}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:{equation}\:{in}\:{the}\:{interval}\:\left[\:−\mathrm{2}\pi;\mathrm{2}\pi\:\right] \\ $$$$\:\:\:{help}\:{please} \\ $$ Answered by…
Question Number 209709 by Ismoiljon_008 last updated on 19/Jul/24 $$ \\ $$$$\:\:\:\int\left({sinx}+{cosx}\right)^{\mathrm{11}} {dx}=\:? \\ $$$$\:\:\:{help}\:{me}\:{please} \\ $$ Answered by mr W last updated on 19/Jul/24…
Question Number 209718 by Ismoiljon_008 last updated on 19/Jul/24 Answered by mr W last updated on 19/Jul/24 $${a}_{{n}} =\frac{\mathrm{1}}{{n}!×\left({n}+\mathrm{2}\right)}=\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)!}−\frac{\mathrm{1}}{\left({n}+\mathrm{2}\right)!} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}{a}_{{n}} =\left(\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}\right)+\left(\frac{\mathrm{1}}{\mathrm{3}!}−\frac{\mathrm{1}}{\mathrm{4}!}\right)+…+\left(\frac{\mathrm{1}}{\mathrm{2024}!}−\frac{\mathrm{1}}{\mathrm{2025}!}\right. \\…