Question Number 211415 by AlagaIbile last updated on 08/Sep/24 Commented by loredcs2357 last updated on 11/Oct/24 $$\mathrm{Let}\:{S}\left({n}\right)=\underset{{k}\leqslant{n}} {\sum}\mathrm{lcm}\left({k},{n}\right). \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{see}\:\mathrm{that}\:{S}\left({n}\right)=\frac{{n}}{\mathrm{2}}\left[\underset{{d}\mid{n}} {\sum}\varphi\left({d}^{\mathrm{2}} \right)+\mathrm{1}\right].\:\mathrm{Moreover}\:\mathrm{we}\:\mathrm{have}: \\ $$$${f}\left({n}\right)=\underset{{d}\mid{n}} {\sum}\varphi\left({d}^{\mathrm{2}}…
Question Number 211414 by AlagaIbile last updated on 08/Sep/24 Answered by Frix last updated on 08/Sep/24 $$\mathrm{Let}\:{x}_{{j}} \leqslant{x}_{{j}+\mathrm{1}} \\ $$$$\frac{\mathrm{1}}{{x}_{\mathrm{1}} }=\mathrm{1}\:\Rightarrow\:\mathrm{max}\:\left({x}_{\mathrm{1}} \right)\:=\mathrm{1} \\ $$$$\frac{\mathrm{1}}{{x}_{\mathrm{1}} }+\frac{\mathrm{1}}{{x}_{\mathrm{2}}…
Question Number 211370 by liuxinnan last updated on 07/Sep/24 $${F}\left(\mathrm{0}\right)=\mathrm{0}\:\:\:\:\:\:\:{F}\left(\mathrm{1}\right)=\mathrm{1}\:\:\:\:{F}\left({n}+\mathrm{1}\right)={F}\left({n}\right)+{F}\left({n}−\mathrm{1}\right) \\ $$$${prove}: \\ $$$$\frac{\mathrm{1}}{\mathrm{89}}=\underset{{i}=\mathrm{1}} {\overset{+\infty} {\sum}}\mathrm{10}^{−{i}} {F}\left({i}−\mathrm{1}\right) \\ $$ Answered by mr W last updated…
Question Number 211383 by zakirullah last updated on 07/Sep/24 Commented by zakirullah last updated on 07/Sep/24 $${please}\:{need}\:{difference}\:{with}\:{solution}. \\ $$ Answered by A5T last updated on…
Question Number 211279 by Davidtim last updated on 04/Sep/24 Commented by Davidtim last updated on 04/Sep/24 $${T}_{\mathrm{1}} =? \\ $$$${T}_{\mathrm{2}} =? \\ $$$${T}_{\mathrm{3}} =? \\…
Question Number 211258 by otchereabdullai@gmail.com last updated on 02/Sep/24 Answered by A5T last updated on 02/Sep/24 $$\Rightarrow{tan}\mathrm{2}\theta=\frac{\mathrm{28}}{\mathrm{9}}\Rightarrow\theta=\frac{{tan}^{−\mathrm{1}} \left(\frac{\mathrm{28}}{\mathrm{9}}\right)}{\mathrm{2}}\approx\mathrm{36}.\mathrm{091}° \\ $$ Terms of Service Privacy Policy…
Question Number 211129 by depressiveshrek last updated on 29/Aug/24 Commented by depressiveshrek last updated on 29/Aug/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{this}\:\mathrm{series} \\ $$ Answered by mr W last updated…
Question Number 211049 by Ghisom last updated on 26/Aug/24 $$\mathrm{someone}\:\mathrm{please}\:\mathrm{try}\:\mathrm{question}\:\mathrm{204666} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210972 by ujah last updated on 25/Aug/24 Answered by TonyCWX08 last updated on 25/Aug/24 $${a}.\: \\ $$$${n}\left({C}\:{only}\right)\:=\:\mathrm{18}−\mathrm{6}−\mathrm{3}=\mathrm{9} \\ $$$$ \\ $$$${b}. \\ $$$${n}\left({One}\:{subject}\:{only}\right)…
Question Number 210989 by mokys last updated on 25/Aug/24 $${prove}\:{tan}\left(\mathrm{72}^{°} \right)={tan}\left(\mathrm{66}^{°} \right)+{tan}\left(\mathrm{36}^{°} \right)+{tan}\left(\mathrm{6}^{°} \right)\:\: \\ $$ Answered by som(math1967) last updated on 26/Aug/24 $${tan}\mathrm{72}={tan}\left(\mathrm{66}+\mathrm{6}\right) \\…