Question Number 194241 by tri26112004 last updated on 01/Jul/23 Answered by mr W last updated on 02/Jul/23 $${assumed}\:{a},{b}\in{N} \\ $$$$\frac{\mathrm{1}}{{n}\left({n}+{a}\right)\left({n}+{b}\right)}=\frac{{A}}{{n}}+\frac{{B}}{{n}+{a}}+\frac{{C}}{{n}+{b}} \\ $$$$\left({A}+{B}+{C}\right){n}^{\mathrm{2}} +\left[\left(\mathrm{2}{a}+{b}\right){A}+{bB}\right]{n}+{abA}=\mathrm{1} \\ $$$${A}+{B}+{C}=\mathrm{0}…
Question Number 194113 by Rupesh123 last updated on 28/Jun/23 Answered by Subhi last updated on 28/Jun/23 $$ \\ $$$$\frac{{a}\left({a}−\mathrm{1}\right)\left({a}−\mathrm{2}\right)…..}{{a}\left({a}−\mathrm{2}\right)\left({a}−\mathrm{4}\right)…..}.\frac{{b}\left({b}−\mathrm{2}\right)\left({b}−\mathrm{4}\right)…}{{b}\left({b}−\mathrm{1}\right)\left({b}−\mathrm{2}\right)….} \\ $$$$\:=\:\frac{\left({a}−\mathrm{1}\right)\left({a}−\mathrm{3}\right)\left({a}−\mathrm{5}\right)…..}{\left({b}−\mathrm{1}\right)\left({b}−\mathrm{3}\right)\left({b}−\mathrm{5}\right)…..}\:\:\:\: \\ $$$$\mathrm{24}\:{can}\:{be}\:{the}\:{multiplication}\:{of}\:{n},\:{n}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{4}\right),\left(\mathrm{6}\right)…
Question Number 194240 by cherokeesay last updated on 01/Jul/23 Answered by BaliramKumar last updated on 01/Jul/23 $$\mathrm{28}\:\checkmark \\ $$ Answered by a.lgnaoui last updated on…
Question Number 194237 by MrGHK last updated on 01/Jul/23 $$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{evaluate}}\: \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{k}^{{n}} {n}!\left({zn}+\mathrm{1}\right)} \\ $$ Commented by TheHoneyCat last updated on 14/Jul/23…
Question Number 194236 by MrGHK last updated on 01/Jul/23 Answered by witcher3 last updated on 03/Jul/23 $$\mathrm{S}=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}!\left(\mathrm{zn}+\mathrm{1}\right)\mathrm{k}^{\mathrm{n}} } \\ $$$$=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\int\left(\frac{−\mathrm{1}}{\mathrm{k}}\right)^{\mathrm{n}} .\frac{\mathrm{1}}{\mathrm{n}!}\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 194238 by cortano12 last updated on 01/Jul/23 Answered by aba last updated on 01/Jul/23 $$\left(\mathrm{2},\mathrm{1}\right)\:\vee\:\left(\mathrm{1},−\mathrm{1}\right)\:\checkmark \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 194226 by BaliramKumar last updated on 30/Jun/23 $$ \\ $$$$\mathrm{If}\:{x}^{\mathrm{2}} \:−\:\mathrm{65}{x}\:=\:\mathrm{64}\sqrt{{x}}\:\mathrm{then}\:\sqrt{{x}\:−\:\sqrt{{x}}\:}\:=\:? \\ $$ Answered by Frix last updated on 30/Jun/23 $${x}^{\mathrm{2}} −\mathrm{65}{x}=\mathrm{64}\sqrt{{x}} \\…
Question Number 194216 by Rupesh123 last updated on 30/Jun/23 Answered by qaz last updated on 01/Jul/23 $$\begin{pmatrix}{\mathrm{2084}}\\{\mathrm{1042}}\end{pmatrix}=\begin{pmatrix}{\mathrm{4}×\mathrm{521}}\\{\mathrm{2}×\mathrm{521}}\end{pmatrix}\equiv\begin{pmatrix}{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}\equiv\mathrm{6}\left({mod}\:\mathrm{521}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 194219 by Shlock last updated on 30/Jun/23 Answered by Frix last updated on 30/Jun/23 $$\left({x}^{\mathrm{3}} +\mathrm{4}{x}−\mathrm{8}\right)\left({x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{8}\right)\left({x}+\mathrm{2}\right)= \\ $$$$={x}^{\mathrm{7}} +\mathrm{64}{x}^{\mathrm{2}} −\mathrm{128} \\…
Question Number 194218 by Mingma last updated on 30/Jun/23 Commented by Frix last updated on 30/Jun/23 $${t}=−\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Commented by Mingma last updated on…