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Category: Algebra

n-1-log-n-n-2-Does-the-series-converge-or-diverge-help-find-the-sum-

Question Number 46527 by Tawa1 last updated on 28/Oct/18 $$\underset{\mathrm{n}=\:\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\:\left(\frac{\mathrm{log}\:\mathrm{n}}{\mathrm{n}}\right)^{\mathrm{2}} \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{series}\:\mathrm{converge}\:\mathrm{or}\:\mathrm{diverge},\:\:\mathrm{help}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:… \\ $$ Commented by maxmathsup by imad last updated on 28/Oct/18…

Question-112058

Question Number 112058 by mohssinee last updated on 05/Sep/20 Answered by MJS_new last updated on 06/Sep/20 $$\Rightarrow\:{x}=−\frac{\mathrm{19}\pm\sqrt{\mathrm{4}{a}^{\mathrm{2}} −\mathrm{407}}}{\mathrm{2}} \\ $$$$\mathrm{4}{a}^{\mathrm{2}} −\mathrm{407}={b}^{\mathrm{2}} \:\mathrm{with}\:{b}\in\mathbb{Z} \\ $$$$\mathrm{4}{a}^{\mathrm{2}} ={b}^{\mathrm{2}}…

solve-for-x-y-z-C-2x-2-3x-13x-2-52x-40-6y-2-14x-x-2-220x-300-z-2-2z-12x-2-72x-132-exact-solutions-possible-in-all-cases-

Question Number 112053 by MJS_new last updated on 05/Sep/20 $$\mathrm{solve}\:\mathrm{for}\:{x},\:{y},\:{z}\:\in\mathbb{C}: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}=\sqrt{\mathrm{13}{x}^{\mathrm{2}} −\mathrm{52}{x}+\mathrm{40}} \\ $$$$\mathrm{6}{y}^{\mathrm{2}} −\mathrm{14}{x}=\sqrt{{x}^{\mathrm{2}} −\mathrm{220}{x}+\mathrm{300}} \\ $$$${z}^{\mathrm{2}} −\mathrm{2}{z}=\sqrt{−\mathrm{12}{x}^{\mathrm{2}} +\mathrm{72}{x}−\mathrm{132}} \\ $$$$\left[\mathrm{exact}\:\mathrm{solutions}\:\mathrm{possible}\:\mathrm{in}\:\mathrm{all}\:\mathrm{cases}\right] \\…

f-x-f-1-1-x-3-1-3-x-3-is-given-find-the-value-of-f-1-

Question Number 177530 by mnjuly1970 last updated on 06/Oct/22 $$ \\ $$$${f}\:\left({x}\:\right)\:+\:{f}\:\left(\frac{\:\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}\:−{x}^{\:\mathrm{3}} }}\:\right)=\:{x}^{\:\mathrm{3}} \\ $$$$\:\:\:\:\:\:{is}\:{given}.\:{find}\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{f}\:\left(−\mathrm{1}\right)=? \\ $$$$ \\ $$ Answered by…

Question-111982

Question Number 111982 by houssam last updated on 05/Sep/20 Answered by aleks041103 last updated on 05/Sep/20 $$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}{a}^{{k}} =\frac{\mathrm{1}}{\mathrm{1}−{a}},\:{for}\:\mid{a}\mid<\mathrm{1} \\ $$$${But}\:{here}\:{a}={i},\:{for}\:{which}\:\mid{a}\mid=\mid{i}\mid=\mathrm{1},\:{which} \\ $$$${means}\:{that}\:{the}\:{sum}\:{doesn}'{t}\:{converge} \\…