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Category: Algebra

Simplify-1-A-B-A-B-2-A-B-A-B-

Question Number 168858 by Shrinava last updated on 19/Apr/22 $$\mathrm{Simplify}: \\ $$$$\mathrm{1}.\:\left(\mathrm{A}\:+\:\mathrm{B}\right)\left(\mathrm{A}\:+\:\overline {\mathrm{B}}\right) \\ $$$$\mathrm{2}.\:\left(\overline {\mathrm{A}}\:+\:\mathrm{B}\right)\left(\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}}\right) \\ $$ Answered by Rasheed.Sindhi last updated…

Prove-that-1-A-B-A-B-AB-A-B-2-A-C-B-C-AB-C-

Question Number 168859 by Shrinava last updated on 19/Apr/22 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{1}.\:\overline {\mathrm{A}\:+\:\mathrm{B}}\:=\:\overline {\mathrm{A}}\:\centerdot\:\overline {\mathrm{B}}\:\:\:,\:\:\:\overline {\mathrm{AB}}\:=\:\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}} \\ $$$$\mathrm{2}.\:\left(\mathrm{A}\:+\:\mathrm{C}\right)\left(\mathrm{B}\:+\:\mathrm{C}\right)\:=\:\mathrm{AB}\:+\:\mathrm{C} \\ $$ Answered by Rasheed.Sindhi…

1-9-1-3-2-9-1-3-4-9-1-3-

Question Number 103286 by bemath last updated on 14/Jul/20 $$\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}}{\mathrm{9}}}−\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}}{\mathrm{9}}}+\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{4}}{\mathrm{9}}}\:=\:? \\ $$ Commented by bemath last updated on 14/Jul/20 $${yes}.\:{thank}\:{both} \\ $$ Answered by floor(10²Eta[1])…

k-0-1-k-k-4-k-2-1-

Question Number 103278 by bachamohamed last updated on 13/Jul/20 $$\:\:\:\:\:\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\boldsymbol{{k}}!\left(\boldsymbol{{k}}^{\mathrm{4}} +\boldsymbol{{k}}^{\mathrm{2}} +\mathrm{1}\right)}=? \\ $$ Commented by Dwaipayan Shikari last updated on 13/Jul/20 $$\mathrm{By}\:\mathrm{ratio}\:\mathrm{test}\:\mathrm{it}\:\mathrm{converges}\:\mathrm{sir}!…

Question-168813

Question Number 168813 by safojontoshtemirov last updated on 18/Apr/22 Answered by aleks041103 last updated on 18/Apr/22 $${We}\:{can}\:{add}\:{and}/{or}\:{subtract}\:{different} \\ $$$${rows}\:{from}\:{each}\:{other}\:{without}\:{changing} \\ $$$${the}\:{determinant}. \\ $$$$\Rightarrow{d}_{{n}} =\begin{vmatrix}{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{2}}&{\ldots}&{\mathrm{2}}&{\mathrm{2}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{\mathrm{3}}&{\mathrm{3}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}&{\vdots}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−\mathrm{1}}&{{n}−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−\mathrm{1}}&{{n}}\end{vmatrix} \\…