Question Number 70044 by naka3546 last updated on 30/Sep/19 $$\sqrt{\mathrm{2016}\:+\:\mathrm{2007}\sqrt{\mathrm{2018}\:+\:\mathrm{2009}\sqrt{\mathrm{2020}\:+\:\mathrm{2011}\sqrt{\mathrm{2022}\:+\:\ldots}}}}\:\:=\:\:… \\ $$ Commented by Prithwish sen last updated on 30/Sep/19 $$\left(\mathrm{a}−\mathrm{6}\right)=\sqrt{\left(\mathrm{a}−\mathrm{6}\right)^{\mathrm{2}} }=\sqrt{\mathrm{a}+\left(\mathrm{a}^{\mathrm{2}} −\mathrm{13a}+\mathrm{36}\right)} \\ $$$$\:\:=\:\sqrt{\mathrm{a}+\left(\mathrm{a}−\mathrm{9}\right)\left(\mathrm{a}−\mathrm{4}\right)}\:=\:\sqrt{\mathrm{a}+\left(\mathrm{a}−\mathrm{9}\right)\sqrt{\left(\mathrm{a}−\mathrm{4}\right)^{\mathrm{2}}…
Question Number 4507 by 123456 last updated on 03/Feb/16 $$\mathrm{lets}\:{a}\:\mathrm{and}\:{b}\:\mathrm{be}\:\mathrm{two}\:\mathrm{sequence}\:\mathrm{such}\:\mathrm{that} \\ $$$${A}=\underset{{n}\rightarrow+\infty} {\mathrm{lim}}{a}_{{n}} \\ $$$${B}=\underset{{n}\rightarrow+\infty} {\mathrm{lim}}{b}_{{n}} \\ $$$$\mathrm{exist}\:\mathrm{and}\:\mathrm{are}\:\mathrm{finite},\:\mathrm{lets} \\ $$$${c}\:\mathrm{be}\:\mathrm{a}\:\mathrm{new}\:\mathrm{sequence} \\ $$$${c}_{{n}} ={p}\left({n}\right){a}_{\sigma\left({n}\right)} +{q}\left({n}\right){b}_{\mu\left({n}\right)} \\…
Question Number 70040 by Shamim last updated on 30/Sep/19 $$\mathrm{If},\:\mathrm{a}^{\mathrm{2}} \mathrm{b}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{c}^{\mathrm{3}} }\right)=\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} \:\mathrm{than} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{Successive}\:\mathrm{Proportional}. \\ $$ Commented by…
Question Number 4505 by Yozzii last updated on 03/Feb/16 Commented by Yozzii last updated on 03/Feb/16 $$\bigtriangleup{ACD}\:{and}\:\bigtriangleup{DBE}\:{are}\:{equilateral}. \\ $$$${F}\:{is}\:{the}\:{midpoint}\:{of}\:{AE}\:{and}\:{G}\:{is}\:{the} \\ $$$${midpoint}\:{of}\:{BC}.\:{D}\:{is}\:{a}\:{point}\:{on}\:{the} \\ $$$${line}\:{AB}.\:{Prove}\:{that}\:\bigtriangleup{FGD}\:{is}\: \\ $$$${equilateral}.\:…
Question Number 135573 by malwan last updated on 14/Mar/21 $$ \\ $$ Commented by malwan last updated on 14/Mar/21 $${happy}\:{pi}\:{day} \\ $$ Commented by malwan…
Question Number 135572 by learner001 last updated on 14/Mar/21 $${does}\:{the}\:{sequence}\:\left\{{a}_{{n}} \right\}\:{defined}\:{by},\:{a}_{{n}} =\begin{cases}{\mathrm{0},\:{if}\:{n}\:{is}\:{odd}}\\{\frac{\mathrm{1}}{{n}},\:{if}\:{n}\:{is}\:{even}}\end{cases}\:\:\:{converge}. \\ $$ Answered by dhgt last updated on 05/May/21 Terms of Service Privacy…
Question Number 4502 by #na last updated on 02/Feb/16 $$\frac{\mathrm{4}}{{x}−\mathrm{1}}−\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}−\frac{\mathrm{2}}{{x}+\mathrm{1}}+\frac{\mathrm{6}}{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$ Answered by Rasheed Soomro last updated on 02/Feb/16 $$\frac{\mathrm{4}}{{x}−\mathrm{1}}−\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}−\frac{\mathrm{2}}{{x}+\mathrm{1}}−\frac{\mathrm{6}}{\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)} \\…
Question Number 4500 by FilupSmith last updated on 02/Feb/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{n}!}{{n}^{{n}} }={L} \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{for}\:{L} \\ $$ Commented by Yozzii last updated on 02/Feb/16…
Question Number 70035 by TawaTawa last updated on 30/Sep/19 Commented by TawaTawa last updated on 30/Sep/19 Commented by mr W last updated on 30/Sep/19 $${let}\:{x}={XP}…
Question Number 135571 by bemath last updated on 14/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}}{\left({k}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{8}}\:=? \\ $$ Commented by EDWIN88 last updated on 14/Mar/21 $$\mathrm{i}\:\mathrm{guess}\:\mathrm{the}\:\mathrm{series}\:\mathrm{should}\:\mathrm{be}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{k}}{\left(\mathrm{k}^{\mathrm{2}}…