Question Number 121567 by mathocean1 last updated on 09/Nov/20 $$\mathrm{Hello}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\: \\ $$$$\mathrm{equation}: \\ $$$$\begin{cases}{\mathrm{3}{x}−{y}\equiv\mathrm{1}\left[\mathrm{5}\right]}\\{{x}+\mathrm{2}{y}\equiv\mathrm{0}\left[\mathrm{5}\right]}\end{cases} \\ $$ Commented by TANMAY PANACEA last updated on 09/Nov/20 $$\left[\mathrm{5}\right]\:\:{what}\:{does}\:\left[\:.\right]\:{means}…
Question Number 187085 by Rupesh123 last updated on 13/Feb/23 Answered by witcher3 last updated on 14/Feb/23 $$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}} \\ $$$$\mathrm{S}_{\mathrm{n}+\mathrm{1}} −\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}+\mathrm{1}}…
Question Number 55992 by Mikael_Marshall last updated on 07/Mar/19 $$\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \:+\:.\:.\:.\:+\:{x}^{\mathrm{99}} =\mathrm{0} \\ $$$${need}\:{an}\:{explanation}. \\ $$ Commented by mr W last updated on 07/Mar/19 $${if}\:{x}=−\mathrm{1}:…
Question Number 121496 by Lordose last updated on 08/Nov/20 $$\mathrm{Are}\:\mathrm{they}\:\mathrm{equal}? \\ $$$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{n}+\mathrm{1}\right)}{\mathrm{n}+\mathrm{1}}\:\mathrm{and}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{n}\right)}{\mathrm{n}} \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 187025 by Rupesh123 last updated on 12/Feb/23 Answered by a.lgnaoui last updated on 12/Feb/23 $${E} \\ $$ Commented by Rupesh123 last updated on…
Question Number 55869 by mr W last updated on 05/Mar/19 $${if}\:\boldsymbol{{a}}_{\boldsymbol{{n}}+\mathrm{2}} =\frac{\boldsymbol{{a}}_{\boldsymbol{{n}}+\mathrm{1}} ^{\mathrm{3}} }{\boldsymbol{{a}}_{\boldsymbol{{n}}} ^{\mathrm{2}} }\:{and}\:{a}_{\mathrm{1}} =\mathrm{2},\:{a}_{\mathrm{2}} =\mathrm{4} \\ $$$${find}\:\boldsymbol{{a}}_{\boldsymbol{{n}}} =? \\ $$ Commented by…
Question Number 186884 by Mingma last updated on 11/Feb/23 Commented by mr W last updated on 11/Feb/23 $${you}\:{are}\:{asking}\:{questions}\:{non}−{stop}, \\ $$$${but}\:{you}\:{seem}\:{never}\:{to}\:{give}\:{any}\:{feed} \\ $$$${back}:\:{no}\:{thanks}\:{to}\:{people}\:{who}\: \\ $$$${answered}\:{your}\:{questions},\:{no}\: \\…
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Question Number 55674 by gunawan last updated on 01/Mar/19 $$\mathrm{The}\:\mathrm{smallest}\:\mathrm{integer}\:\mathrm{numbers} \\ $$$$\mathrm{with}\:{n}\:\geqslant\:\mathrm{2018}\:\mathrm{so} \\ $$$$\left(\sqrt{\mathrm{3}}+\mathrm{3}{i}\right)^{{n}} \:\mathrm{form}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{is}.. \\ $$ Answered by mr W last updated on 02/Mar/19…
Question Number 55628 by Mikael_Marshall last updated on 28/Feb/19 $${In}\:{an}\:{A}.{P},\:{the}\:{sum}\:{of}\:{the}\:{first}\:\mathrm{50}\:{terms}\:{is}\:\mathrm{6275}.\:{Write}\:\:{this}\:{A}.{P}\:.\:{knowing}\:{that}\:{the}\:{ratio}\:{is}\:\mathrm{5}. \\ $$ Answered by kaivan.ahmadi last updated on 28/Feb/19 $${s}_{{n}} =\frac{{n}}{\mathrm{2}}\left[\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right] \\ $$$$\mathrm{6275}=\mathrm{25}\left[\mathrm{2}{a}+\mathrm{49}×\mathrm{5}\right]=\mathrm{25}\left[\mathrm{2}{a}+\mathrm{245}\right]= \\ $$$$\mathrm{50}{a}+\mathrm{6145}\Rightarrow\mathrm{50}{a}=\mathrm{6275}−\mathrm{6145}=\mathrm{150}\Rightarrow…