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Question-199547

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}! \\…

2-7-12-x-270-Find-x-

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)…

I-0-pi-2-tan-1-sinx-2-dx-

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}}…

calculate-Q-lim-x-pi-4-1-sin-x-cos-x-tan-2x-Nice-Mathematics-

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…

if-a-n-is-geometric-sequence-and-we-know-p-n-m-2-S-p-f-a-n-a-m-n-m-Attention-The-purpose-of-obtaining-a-relationship-without-the-need-for-direct-calculation-is-the-common-rat

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…