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Category: Algebra

S-n-4-n-1-1-n-2-

Question Number 127344 by bobhans last updated on 29/Dec/20 $${S}\:=\:\underset{{n}=\mathrm{4}} {\overset{\infty} {\sum}}\ell{n}\:\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\:=?\: \\ $$ Answered by liberty last updated on 29/Dec/20 $$\:{S}\:=\:\underset{{n}=\mathrm{4}} {\overset{\infty} {\sum}}\mathrm{ln}\:\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}}…

if-a-b-c-d-63-and-a-b-c-d-N-find-the-maximum-value-of-ab-bc-cd-

Question Number 192856 by universe last updated on 29/May/23 $$\:{if}\:{a}+{b}+{c}\:+{d}\:\:=\:\mathrm{63}\:{and}\:{a},{b},{c},{d}\:\in\:\mathbb{N}\:{find}\: \\ $$$$\:\:\:{the}\:{maximum}\:{value}\:{of}\:{ab}+{bc}+{cd}\:=\:? \\ $$ Answered by Frix last updated on 29/May/23 $$\mathrm{32}+\mathrm{31}+\mathrm{0}+\mathrm{0}=\mathrm{63} \\ $$$$\mathrm{32}×\mathrm{31}=\mathrm{992} \\…

find-the-domain-of-thefunction-f-x-1-x-2-x-2-where-is-the-fractional-part-function-

Question Number 192852 by York12 last updated on 29/May/23 $$ \\ $$$${find}\:{the}\:{domain}\:{of}\:{thefunction} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left\{{x}\right\}^{\mathrm{2}} }}\:\:\:\:\:{where}\:\left\{.\right\}\:{is}\:{the}\:{fractional}\:{part}\:{function}. \\ $$ Commented by York12 last updated on 30/May/23…

Question-192855

Question Number 192855 by pascal889 last updated on 29/May/23 Answered by a.lgnaoui last updated on 29/May/23 $$\begin{cases}{\mathrm{P}^{\mathrm{2}} −\mathrm{2aP}−\mathrm{10P}+\mathrm{2a}^{\mathrm{2}} +\mathrm{6a}\:\:−\mathrm{6}=\mathrm{0}\:\:\left(\mathrm{1}\right)}\\{\mathrm{P}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{27P}\:\:\:\:\:\:\:\:\:+\mathrm{27a}−\mathrm{27}=\mathrm{0}\:\:\left(\mathrm{2}\right)\:}\end{cases} \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right)\Rightarrow\:\mathrm{2a}^{\mathrm{2}} −\mathrm{21a}+\mathrm{21}+\mathrm{P}\left(\mathrm{17}−\mathrm{2a}\right)=\mathrm{0} \\ $$$$…

Question-192839

Question Number 192839 by Mingma last updated on 29/May/23 Answered by witcher3 last updated on 02/Jun/23 $$\mathrm{we}\:\mathrm{see}\:\mathrm{that}\:\mathrm{2},\mathrm{7}\:\mathrm{can}'\mathrm{t}\:\mathrm{bee}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{n} \\ $$$$\mathrm{and}\:\mathrm{11}\mid\mathrm{n}\: \\ $$$$\mathrm{if}\:\mathrm{n}≢\mathrm{0}\left[\mathrm{11}\right] \\ $$$$\frac{\mathrm{n}^{\mathrm{2}} +\mathrm{4}^{\mathrm{n}} +\mathrm{7}^{\mathrm{n}}…