Question Number 52677 by maxmathsup by imad last updated on 11/Jan/19 $${find}\:{nature}\:{of}\:\sum_{{n}=\mathrm{2}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} \sqrt{{n}}{ln}\left(\frac{{n}+\mathrm{1}}{{n}−\mathrm{1}}\right). \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 52678 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{u}_{{n}} ={ln}\left\{{cos}\left(\mathrm{2}^{−{n}} \right)\right\}\:\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{u}_{{n}} \\ $$ Commented by Abdo msup. last updated on…
Question Number 52675 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{u}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{{n}} {xdx}\:\:{calculate}\:\Sigma\:{u}_{{n}} \\ $$ Commented by maxmathsup by imad last…
Question Number 52673 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{f}\left({x}\right)=\left({x}^{{n}} −\mathrm{1}\right){e}^{{x}} \:\:\:{determine}\:{f}^{\left({n}\right)} \left({x}\right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 52671 by maxmathsup by imad last updated on 11/Jan/19 $${study}\:{the}\:{sequence}\:{u}_{\mathrm{0}} =\mathrm{1}\:{and}\:{u}_{{n}+\mathrm{1}} \:\:=\frac{\mathrm{1}}{\mathrm{1}+{u}_{{n}} ^{\mathrm{2}} } \\ $$ Commented by maxmathsup by imad last updated…
Question Number 52669 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{S}_{{n}\:} \:\left({p}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{{p}} \\ $$$${prove}\:{that}\:{S}_{{n}} \left({p}\right)=\frac{\mathrm{1}}{{p}+\mathrm{1}}\left\{\:\left({n}+\mathrm{1}\right)^{{p}+\mathrm{1}} \:−\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{p}+\mathrm{1}} ^{{k}} \:{S}_{{n}} \left({k}\right)\right\} \\…
Question Number 52670 by maxmathsup by imad last updated on 11/Jan/19 $${study}\:{the}\:{convergence}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}\left(\pi\sqrt{\mathrm{4}{n}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 183712 by Michaelfaraday last updated on 29/Dec/22 $${solve}: \\ $$$${W}\left({In}\left(\mathrm{4}{x}\right)\right)=\sqrt{\left({x}−\mathrm{1}\right)} \\ $$ Answered by mr W last updated on 29/Dec/22 $${e}^{\mathrm{ln}\:\left(\mathrm{4}{x}\right)} \mathrm{ln}\:\left(\mathrm{4}{x}\right)=\sqrt{{x}−\mathrm{1}} \\…
Question Number 118150 by bobhans last updated on 15/Oct/20 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{function}\:\mathrm{f}:\mathbb{R}\diagdown\left\{\mathrm{0},\mathrm{1}\right\}\:\rightarrow\mathbb{R} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{functional}\:\mathrm{relation} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}\right)\:=\:\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}\right)};\:\mathrm{for}\:\mathrm{x}\neq\mathrm{0}\:\mathrm{and}\:\mathrm{x}\neq\mathrm{1} \\ $$ Commented by bemath last updated on 15/Oct/20 $${good}\:{question} \\…
Question Number 117857 by bemath last updated on 14/Oct/20 $$\mathrm{Let}\:\mathrm{n}\in\mathbb{N}\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{polynomials}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{with}\:\mathrm{coefficients} \\ $$$$\mathrm{in}\:\left\{\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\:\right\}\:\mathrm{such}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{2}\right)=\:\mathrm{n}\: \\ $$ Answered by mindispower last updated on 14/Oct/20 $${let}\:{p}\left({x}\right)=\underset{{k}\leqslant{n}} {\sum}{a}_{{k}}…