Question Number 210515 by hardmath last updated on 11/Aug/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{11}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{13}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{17}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{19}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{23}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{29}^{\mathrm{2}} }\:+\:…\:=\:? \\ $$ Commented by mr W…
Question Number 210508 by hardmath last updated on 11/Aug/24 Answered by mr W last updated on 11/Aug/24 Commented by mr W last updated on 11/Aug/24…
Question Number 210533 by hardmath last updated on 11/Aug/24 Commented by mr W last updated on 12/Aug/24 $${typo}\:{AD}\centerdot\frac{\cancel{{m}}\:{n}}{{m}+{n}}−{AB}\centerdot\frac{{q}}{{p}+{q}}\:? \\ $$ Answered by mr W last…
Question Number 210496 by lmcp1203 last updated on 11/Aug/24 Commented by mr W last updated on 11/Aug/24 $${has}\:{that}\:{bracket}\:{a}\:{special}\:{meaning}? \\ $$ Commented by lmcp1203 last updated…
Question Number 210457 by peter frank last updated on 09/Aug/24 Commented by peter frank last updated on 09/Aug/24 $$\left(\mathrm{b}\right)\:\mathrm{and}\:\left(\mathrm{c}\right)\:\mathrm{help} \\ $$ Commented by mr W…
Question Number 210439 by universe last updated on 09/Aug/24 Commented by universe last updated on 09/Aug/24 $${prove}\:{that}\:{the}\:{sequence}\:{is}\:{bounded}\:{and}\: \\ $$$${convergent} \\ $$ Answered by aleks041103 last…
Question Number 210467 by maths_plus last updated on 09/Aug/24 $$\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+…+\sqrt{\mathrm{n}}\:\:\:\mathrm{irrational}\:??? \\ $$ Answered by Frix last updated on 10/Aug/24 $$\mathrm{Yes}!!! \\ $$ Commented by maths_plus…
If-the-roots-of-the-quadratic-equation-a-b-c-x-2-c-b-a-x-2-b-c-0-are-real-and-equal-then-find-a-b-c-
Question Number 210362 by MATHEMATICSAM last updated on 10/Sep/24 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left({a}\:−\:{b}\:+\:{c}\right){x}^{\mathrm{2}} \:+\:\left({c}\:−\:{b}\:−\:{a}\right){x}\:+\:\mathrm{2}\left({b}\:−\:{c}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{and}\:\mathrm{equal}\:\mathrm{then}\:\mathrm{find}\:\frac{{a}}{{b}\:−\:{c}}\:. \\ $$ Commented by som(math1967) last updated on 08/Aug/24 $${not}\:{qudratic}\:,{it}\:{should}\:{be}\:\left({a}−{b}+{c}\right){x}^{\mathrm{2}}…
Question Number 210392 by peter frank last updated on 08/Aug/24 Commented by mr W last updated on 09/Aug/24 $${in}\:\left({b}\right)\:{it}\:{is}\:\frac{\mathrm{1}}{\mathrm{7}},\:{not}\:\frac{\mathrm{1}}{\mathrm{4}}. \\ $$ Answered by mr W…
Question Number 210390 by hardmath last updated on 08/Aug/24 Answered by Berbere last updated on 08/Aug/24 $${t}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}\right)={f}\left({t}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{1}\Rightarrow\exists{M}\in\mathbb{R}_{+} \:\forall{x}\geqslant{M}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant{f}\left({x}\right)\leqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow\forall{x}\geqslant{M} \\…