Question Number 199547 by hardmath last updated on 05/Nov/23 Answered by mr W last updated on 05/Nov/23 $$\left.\mathrm{1}\right) \\ $$$${n}×{n}!=\left({n}+\mathrm{1}−\mathrm{1}\right)×{n}!=\left({n}+\mathrm{1}\right)!−{n}! \\ $$$$\mathrm{1}×\mathrm{1}!+\mathrm{2}×\mathrm{2}!+…+\mathrm{2022}×\mathrm{2022}! \\ $$$$=\mathrm{2}!−\mathrm{1}!+\mathrm{3}!−\mathrm{2}!+….+\mathrm{2023}!−\mathrm{2022}! \\…
Question Number 199606 by essaad last updated on 05/Nov/23 Answered by cortano12 last updated on 06/Nov/23 $$\:\mathrm{L}\:=\:\infty\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 199568 by ajfour last updated on 05/Nov/23 Commented by ajfour last updated on 05/Nov/23 $${Hence}\:{what}\:{is}\:{m}\:\:{if}\:\:{x}={a}={mb} \\ $$ Answered by ajfour last updated on…
Question Number 199602 by hardmath last updated on 05/Nov/23 $$\mathrm{2}\:+\:\mathrm{7}\:+\:\mathrm{12}\:+\:…\:+\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{270} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 06/Nov/23 $${a}=\mathrm{2},{d}=\mathrm{5} \\ $$$${S}_{{n}} =\frac{{n}}{\mathrm{2}}\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right)…
Question Number 199570 by universe last updated on 05/Nov/23 $$\:\:\:\:\:\:\:\:\mathrm{I}\:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}{x}\:}{\mathrm{2}}\right){dx} \\ $$ Answered by witcher3 last updated on 05/Nov/23 $$\mathrm{I}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{tan}^{−\mathrm{1}}…
Question Number 199597 by mnjuly1970 last updated on 05/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{Q}\::\:\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\frac{\pi}{\mathrm{4}}} \:\:\left(\:\:\mathrm{1}\:+\:\:{sin}\left({x}\right)\:−{cos}\left({x}\right)\:\right)^{\:{tan}\left(\mathrm{2}{x}\right)} \:=\:\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet\:\mathscr{N}{ice}\:−\:\mathscr{M}{athematics}\:\bullet\: \\ $$$$\:\:\:\:\:\:\: \\ $$ Answered…
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Question Number 199592 by hardmath last updated on 05/Nov/23 Commented by mr W last updated on 06/Nov/23 $${impossible}!\:{you}\:{can}\:{not}\:{get}\:{a}\:{sum}\:{of} \\ $$$$\mathrm{270}\:! \\ $$ Commented by mr…
Question Number 199593 by jabarsing last updated on 05/Nov/23 $${if}\:\left\{{a}_{{n}} \right\}\:{is}\:{geometric}\:{sequence}\:{and}\: \\ $$$$ \\ $$$${we}\:{know}\:,\:{p}=\frac{{n}+{m}}{\mathrm{2}}\:\:\Rightarrow \\ $$$$\:{S}_{{p}} \:=\:{f}\left({a}_{{n}} ,{a}_{{m}} ,{n},{m}\right)=? \\ $$$$\blacksquare{Attention}:\: \\ $$The purpose…
Question Number 199553 by cortano12 last updated on 05/Nov/23 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)}{\mathrm{x}^{\mathrm{2}} \:\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{2}}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{2}}\:\right)}\:=? \\ $$ Answered by MM42 last updated on 05/Nov/23 $$−\frac{\sqrt{\mathrm{2}}}{\mathrm{8}}\:{i}\:\:\checkmark \\…