Question Number 3565 by Yozzii last updated on 15/Dec/15 $${Define}\:{the}\:{sequence}\:\left\{{a}_{{n}} \right\}\:{by}\:{the} \\ $$$${recurrence}\:{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}_{{n}+\mathrm{1}} ={pa}_{{n}} +{qa}_{{n}−\mathrm{1}} \:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$${where}\:{p},{q}\in\mathbb{C}−\left\{\mathrm{0}\right\}\:{and}\: \\ $$$${a}_{\mathrm{0}} =\alpha\:,\:{a}_{\mathrm{1}} =\beta\:\: \\…
Question Number 3564 by Yozzii last updated on 15/Dec/15 $${Test}\:{for}\:{convergence}: \\ $$$$\left(\mathrm{1}\right)\:\underset{{n}=\mathrm{10}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{\mathrm{ln}\left(\mathrm{ln}{n}\right)} }{{n}\mathrm{ln}{n}} \\ $$$$\left(\mathrm{2}\right)\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left(\mathrm{ln}{n}\right)^{\mathrm{p}} }\:\left(\mathrm{two}\:\mathrm{cases}\:\mathrm{of}\:\mathrm{p}\:\mathrm{to}\:\mathrm{look}\:\mathrm{at}\right) \\ $$$$\left(\mathrm{3}\right)\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \sqrt{{n}}}{\mathrm{ln}{n}}…
Question Number 69098 by rajesh4661kumar@gmail.com last updated on 20/Sep/19 Commented by Kunal12588 last updated on 20/Sep/19 $${its}\:{really}\:{easy}\:{just}\:{construct}\:{a}\:{line}\:{through} \\ $$$${F}\:{parallel}\:{to}\:{AB}\:\&\:{CD}.\:{and}\:{remember}\:{the} \\ $$$${property}\:{of}\:{alternate}\:{interior}\:{angles}\:{and} \\ $$$${consectutive}\:{interior}\:{angles} \\ $$…
Question Number 69092 by Mr. K last updated on 19/Sep/19 Answered by mr W last updated on 21/Sep/19 Commented by mr W last updated on…
Question Number 134630 by mathmax by abdo last updated on 06/Mar/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{u}_{\mathrm{n}} \mathrm{wich}\:\mathrm{verify}\:\mathrm{u}_{\mathrm{n}} +\mathrm{u}_{\mathrm{n}+\mathrm{1}} =\mathrm{cosn} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 134627 by bobhans last updated on 05/Mar/21 $$\mathcal{ALGEBRA} \\ $$If Bobby walks to school at 50m/min. He will be late for 3 minutes.…
Question Number 134621 by bobhans last updated on 05/Mar/21 $$\mathrm{Geometry} \\ $$If a triangle with side lengths 8, 15 and 17 can be inscribed in…
Question Number 3551 by prakash jain last updated on 15/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathbb{P}\:\mathrm{set}\:\mathrm{of}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{is} \\ $$$$\mathrm{countable}. \\ $$ Commented by Filup last updated on 15/Dec/15 $$\mathrm{ah},\:\mathrm{i}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{question}\:\mathrm{now}. \\ $$$$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{answer}\:\mathrm{it},\:\mathrm{though}…
Question Number 134623 by bobhans last updated on 05/Mar/21 $$\mathscr{PR}\mathrm{obability} \\ $$An urn contains 3 red balls, 2 green balls and 1 yellow ball. Three…
Question Number 134622 by bobhans last updated on 05/Mar/21 $$\mathrm{Probability} \\ $$Initially there are 4 red balls and 3 yellow balls in a bag, however…