Question Number 43546 by maxmathsup by imad last updated on 11/Sep/18 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{\:\sqrt{{k}^{\mathrm{2}} \:+{n}^{\mathrm{2}} }}\:\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$ Answered by behi83417@gmail.com last updated…
Question Number 43541 by abdo.msup.com last updated on 11/Sep/18 $${let}\:{u}_{\mathrm{0}} ={u}_{\mathrm{1}} =\mathrm{1}\:{and}\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} \:+{u}_{{n}−\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{u}_{{n}} \\ $$$$\left.\mathrm{3}\right){let}\:{x}_{\mathrm{0}} \:\:{the}\:{positif}\:{roots}\:{of}\:{x}^{\mathrm{2}} ={x}+\mathrm{1} \\ $$$$\left.\mathrm{4}\right)\:{prove}\:{that}\:\forall{n}\geqslant\mathrm{2}\:\:{x}_{\mathrm{0}} ^{{n}−\mathrm{2}} \leqslant{u}_{{n}} \leqslant{x}_{\mathrm{0}}…
Question Number 43537 by abdo.msup.com last updated on 11/Sep/18 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{e}^{\frac{{k}}{{n}}} }{{n}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {S}_{{n}} \\ $$ Commented by maxmathsup by imad last…
Question Number 174570 by blackmamba last updated on 04/Aug/22 $$\:\:\:\:\:\:\begin{cases}{\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}\right)=\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{{x}}^{\mathrm{4}} +\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}}\\{\boldsymbol{{f}}\left(\sqrt{\mathrm{3}}\:\right)=?}\end{cases} \\ $$ Commented by infinityaction last updated on 04/Aug/22 $$\:\:\:{f}\left(\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{{x}}}\right)\:=\:\frac{\mathrm{1}}{\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} }…
Question Number 174469 by Mathspace last updated on 01/Aug/22 $${f}\left({x}\right)=\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)….\left({x}+{n}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right)\:\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right){decompose}\:{F}=\frac{\mathrm{1}}{{f}} \\ $$ Answered by Ar Brandon last updated on 01/Aug/22…
Question Number 108888 by bemath last updated on 20/Aug/20 $$\:\:\:\frac{\vdots\mathcal{B}{e}\mathcal{M}{ath}\vdots}{\bigtriangleup} \\ $$$${Suppose}\:\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{14}{x}−\mathrm{5}=\:\left({Px}+{Q}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{1}\right)+{R}\:{for}\:{all} \\ $$$${value}\:{of}\:{x}.\:{Find}\:{the}\:{value}\:{of}\:{P},{Q}\:{and}\:{R}\: \\ $$ Answered by Rasheed.Sindhi last updated on 20/Aug/20…
Question Number 174373 by Mathspace last updated on 31/Jul/22 $${find}\:\int\sqrt{{x}+\sqrt{\mathrm{1}−{x}}}{dx} \\ $$ Commented by MJS_new last updated on 31/Jul/22 $$\mathrm{see}\:\mathrm{question}\:\mathrm{174341} \\ $$ Terms of Service…
Question Number 43259 by maxmathsup by imad last updated on 08/Sep/18 $${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 43260 by maxmathsup by imad last updated on 08/Sep/18 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} \:−\mathrm{1}}\:. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 108711 by mathmax by abdo last updated on 18/Aug/20 $$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\left(−\mathrm{1}\right)^{\mathrm{2}\left[\mathrm{x}\right]−\mathrm{1}} \mathrm{cos}\left(\mathrm{n}\left[\mathrm{x}\right]\right)\mathrm{dx} \\ $$$$\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$ Answered by mathmax by abdo…