Category: Algebra

Question Number 147344 by mathdanisur last updated on 20/Jul/21 $$\underset{{n}\rightarrow\infty} {{lim}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{log}\:\left(\frac{\mathrm{1}+{sin}^{\boldsymbol{{n}}} \boldsymbol{{x}}}{\mathrm{1}+{x}+{x}^{\boldsymbol{{n}}} }\right){dx}\:=\:? \\ $$ Answered by mathmax by abdo last updated on…

Question Number 147312 by mathdanisur last updated on 19/Jul/21 Answered by Olaf_Thorendsen last updated on 19/Jul/21 $$\mathrm{A}+\mathrm{B}\:=\:\mathrm{AB} \\ $$$$\Leftrightarrow\:\mathrm{AB}−\mathrm{A}−\mathrm{B}\:=\:\overset{\sim} {\mathrm{0}} \\ $$$$\Leftrightarrow\:\mathrm{AB}−\mathrm{A}−\mathrm{B}+\mathrm{I}_{{n}} \:=\:\mathrm{I}_{{n}} \\ $$$$\Leftrightarrow\:\left(\mathrm{A}−\mathrm{I}_{{n}}…

Question Number 16238 by e20160022 last updated on 19/Jun/17 $${we}\:{have}\:{a}^{\mathrm{5}} +{b}^{\mathrm{5}} =\mathrm{1}\:{and}\:{u}^{\mathrm{5}} +{v}^{\mathrm{5}} =\mathrm{1} \\ $$$${find}\:{value}\:\:{a}^{\mathrm{3}} {u}^{\mathrm{5}} +{b}^{\mathrm{3}} {v}^{\mathrm{5}} =? \\ $$ Terms of Service…

Question Number 81768 by Power last updated on 15/Feb/20 Commented by mathmax by abdo last updated on 15/Feb/20 $${S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{k}}{\left({k}+\mathrm{1}\right)!}\:=\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{k}+\mathrm{1}−\mathrm{1}}{\left({k}+\mathrm{1}\right)!}\:=\sum_{{k}=\mathrm{1}} ^{{n}}…

Question Number 81759 by peter frank last updated on 15/Feb/20 Commented by JDamian last updated on 15/Feb/20 $${What}\:{are}\:{the}\:\boldsymbol{{spinning}}\:\boldsymbol{{coefficient}}\:{and} \\ $$$${the}\:\boldsymbol{{luctus}}\:\boldsymbol{{rectum}}\:{of}\:{a}\:{parabola}? \\ $$ Terms of Service…