Question Number 155461 by Jonathanwaweh last updated on 30/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89920 by akash4081 last updated on 20/Apr/20 $${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+{x}}}\:{and}\:{y}=\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{1}+{y}\:}}\:{find}\:{x}+{y} \\ $$ Commented by john santu last updated on 20/Apr/20 $${x}\:=\:\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\:\Rightarrow\:{x}\:=\:\frac{−\mathrm{1}\:\pm\:\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${y}\:=\:\frac{\mathrm{2}\left({y}+\mathrm{1}\right)}{\mathrm{2}{y}+\mathrm{3}}\:\Rightarrow\:{y}\:=\:\frac{−\mathrm{1}\:\pm\:\sqrt{\mathrm{17}}}{\mathrm{4}} \\ $$$$\therefore\:{x}+{y}\:=\:\left(\frac{−\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}}\right)+\left(\frac{−\mathrm{1}\pm\sqrt{\mathrm{17}}}{\mathrm{4}}\right)…
Question Number 155436 by talminator2856791 last updated on 03/Oct/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\underset{{n}=\mathrm{0}} {\overset{{m}} {\sum}}\:\mathrm{10}^{{n}} +\:{m}} \\ $$$$\: \\ $$ Terms of Service Privacy…
Question Number 89907 by necxxx last updated on 19/Apr/20 $${If}\:{the}\:{sum}\:{of}\:\mathrm{4}\:{numbers}\:{is}\:{between} \\ $$$$\mathrm{53}\:{and}\:\mathrm{57}\:{then}\:{the}\:{arithmetic}\:{mean}\:{of} \\ $$$${the}\:{numbers}\:{could}\:{be}\:{one}\:{of}\:{the} \\ $$$${following} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{1}\left..\mathrm{5}\:{b}\right)\mathrm{12}\:{c}\right)\mathrm{12}.\mathrm{5}\:{d}\right)\mathrm{13}\:{e}\right)\mathrm{14} \\ $$ Answered by MJS…
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Question Number 24360 by math solver last updated on 16/Nov/17 Commented by math solver last updated on 25/Nov/17 $$\mathrm{plz}\:\mathrm{help}? \\ $$$$??? \\ $$ Terms of…
Question Number 24359 by math solver last updated on 16/Nov/17 Commented by ajfour last updated on 17/Nov/17 $${If}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{9}{r}^{\mathrm{2}} +\mathrm{3}{r}−\mathrm{1}}\right) \\ $$$$\:\:\:\:=\mathrm{cot}^{−\mathrm{1}} \left(\frac{{m}}{{n}}\right)\:,\:{then}\:{it}\:{means}…
Question Number 155420 by amin96 last updated on 30/Sep/21 $$\frac{\mathrm{1}}{\mathrm{42}}+\frac{\mathrm{1}}{\mathrm{72}}+\frac{\mathrm{1}}{\mathrm{110}}+\ldots=? \\ $$ Answered by puissant last updated on 01/Oct/21 $${S}=\frac{\mathrm{1}}{\mathrm{42}}+\frac{\mathrm{1}}{\mathrm{72}}+\frac{\mathrm{1}}{\mathrm{110}}+…….=\frac{\mathrm{1}}{\mathrm{6}}−\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{9}}+…. \\ $$$$\Rightarrow\:{S}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{2}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)}=\frac{\mathrm{1}}{\mathrm{4}}\underset{{n}=\mathrm{2}} {\overset{\infty}…
Question Number 155393 by cortano last updated on 30/Sep/21 $$\:\:\mid\mid\mathrm{x}−\mathrm{4}\mid−\mathrm{4}\mid\:\geqslant\:\mathrm{4}\: \\ $$ Answered by mr W last updated on 30/Sep/21 $$\mid{x}−\mathrm{4}\mid−\mathrm{4}\geqslant\mathrm{4}\: \\ $$$$\Rightarrow\mid{x}−\mathrm{4}\mid\geqslant\mathrm{8}\: \\ $$$$\Rightarrow{x}−\mathrm{4}\geqslant\mathrm{8}\:{or}\:{x}−\mathrm{4}\leqslant−\mathrm{8}\:…
Question Number 155386 by mathdanisur last updated on 29/Sep/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{H}_{\boldsymbol{\mathrm{k}}} \right)^{\mathrm{3}} }{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }\:=\:\frac{\mathrm{3}\zeta\left(\mathrm{3}\right)\:+\:\mathrm{ln}^{\mathrm{3}} \mathrm{2}\:+\:\pi^{\mathrm{2}} \mathrm{ln2}}{\mathrm{3}}\:\: \\ $$ Answered by Kamel last…