Question Number 166515 by greogoury55 last updated on 21/Feb/22 $$\:\:\:\:{Given}\:{a}\:{function}\: \\ $$$$\:\:\:\left({x}+\mathrm{1}\right){f}\left(−{x}\right)+\frac{\mathrm{1}−{x}}{\mathrm{4}{x}}\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{100}\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{{x}} \\ $$$$\:{x}\neq\mathrm{0}\:,\:{x}\neq\mathrm{1} \\ $$$$\:{Find}\:{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{4}\right)+…+{f}\left(\mathrm{400}\right) \\ $$ Answered by nurtani last updated on…
Question Number 166319 by cortano1 last updated on 18/Feb/22 Commented by otchereabdullai@gmail.com last updated on 18/Feb/22 $$\mathrm{nice}\:\mathrm{question} \\ $$ Commented by MJS_new last updated on…
Question Number 100769 by Rio Michael last updated on 28/Jun/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{sequences}\:\left({u}_{{n}} \right)\:\mathrm{and}\:\left({v}_{{n}} \right)\:\mathrm{defined}\:\mathrm{by} \\ $$$$\:\begin{cases}{{u}_{\mathrm{0}} \:=\:\mathrm{1}}\\{{u}_{{n}+\mathrm{1}} \:=\:\frac{\mathrm{2}{u}_{{n}} {v}_{{n}} }{{u}_{{n}} \:+\:{v}_{{n}} }}\end{cases}\:\mathrm{and}\:\begin{cases}{{v}_{\mathrm{0}} \:=\:\mathrm{2}}\\{{v}_{{n}+\mathrm{1}} \:=\:\frac{{u}_{{n}} \:+\:{v}_{{n}} }{\mathrm{2}}}\end{cases}\:\:\forall\:{n}\in\:\mathbb{N}…
Question Number 100767 by Rio Michael last updated on 28/Jun/20 $$\:\mathrm{sketch}\:\:{x}^{\mathrm{2}} \:=\:{y}^{\mathrm{3}} \:\mathrm{and}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{16} \\ $$$$\mathrm{and}\:\mathrm{hence}\:\mathrm{solve}\:\left({x}^{\mathrm{2}} −{y}^{\mathrm{3}} \right)\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} −\mathrm{16}\right)\:\geqslant\mathrm{0} \\ $$ Answered by…
Question Number 35150 by Victor31926 last updated on 16/May/18 Answered by Rasheed.Sindhi last updated on 16/May/18 $$\bullet\mathrm{Any}\:\mathrm{power}\:\mathrm{of}\:\mathrm{even}\:\mathrm{number}\:\mathrm{is}\:\mathrm{even} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{even}\:\mathrm{number}\:\mathrm{gives}\:\mathrm{remainder}\:\mathrm{0} \\ $$$$\:\:\:\:\:\mathrm{on}\:\mathrm{dividing}\:\mathrm{by}\:\mathrm{2} \\ $$$$\bullet\mathrm{Any}\:\mathrm{power}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{number}\:\mathrm{is}\:\mathrm{odd} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{odd}\:\mathrm{number}\:\mathrm{gives}\:\mathrm{remainder}\:\mathrm{1}…
Question Number 100640 by pticantor last updated on 27/Jun/20 $${let}\left(\:\boldsymbol{{U}}_{{n}} \right)\:{be}\:{a}\:{sequence}\:{definied}\:{by}: \\ $$$$\begin{cases}{\boldsymbol{{U}}_{\mathrm{0}} =\mathrm{1}}\\{\boldsymbol{{U}}_{{n}+\mathrm{1}} =\frac{\mathrm{3}\boldsymbol{{U}}_{\boldsymbol{{n}}} +\mathrm{2}}{\boldsymbol{{U}}_{\boldsymbol{{n}}} +\mathrm{2}}}\end{cases} \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\mathrm{0}<\boldsymbol{{U}}_{\boldsymbol{{n}}} <\mathrm{2} \\ $$ Answered by maths…
Question Number 35036 by abdo mathsup 649 cc last updated on 14/May/18 $${cslculate}\:\sum_{{k}=\mathrm{1}} ^{{n}} {k}^{\mathrm{2}} \left({n}+\mathrm{1}−{k}\right) \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 14/May/18…
Question Number 35035 by abdo mathsup 649 cc last updated on 14/May/18 $${calculate}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 14/May/18…
Question Number 100297 by Coronavirus last updated on 26/Jun/20 $${calulate}\:{using}\:{Riemann}\:{sums} \\ $$$${tbe}\:{limit}\:{of}\:{this}\:{sequence} \\ $$$$\:\:\underset{{k}={n}} {\overset{\mathrm{2}{n}} {\sum}}\mathrm{sin}\:\left(\frac{\pi}{{k}}\right) \\ $$ Answered by abdomsup last updated on 26/Jun/20…
Question Number 100270 by Coronavirus last updated on 25/Jun/20 Answered by abdomsup last updated on 26/Jun/20 $${A}_{{n}} =\sum_{{k}={n}} ^{\mathrm{2}{n}} \:\frac{\pi}{{k}}\:=_{{p}={k}−{n}} \pi\:\sum_{{p}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{{p}+{n}} \\ $$$$=\frac{\pi}{{n}}\sum_{{p}=\mathrm{0}}…