Question Number 76207 by mr W last updated on 25/Dec/19 $${if}\:{a}_{\mathrm{1}} =\mathrm{1}\:{and}\:{a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +{n}^{\mathrm{2}} \\ $$$${find}\:{a}_{{n}} =? \\ $$ Answered by mind is power last…
Question Number 10670 by FilupS last updated on 22/Feb/17 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\zeta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{n}^{−{s}} =\underset{{p}\in\mathbb{P}} {\overset{\infty} {\prod}}\left(\mathrm{1}−{p}^{−{s}} \right)^{−\mathrm{1}} \\ $$ Terms of Service Privacy Policy…
Question Number 10669 by mrW1 last updated on 22/Feb/17 $$\int\sqrt{{a}^{\mathrm{2}} −\mathrm{cos}^{\mathrm{2}} \:{x}\:}{dx}=?\:\:\:\left({a}\geqslant\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10667 by Gaurav3651 last updated on 22/Feb/17 $${prove}\:{that}\:{the}\:{quadrilateral}\:{formed} \\ $$$${by}\:{angle}\:{bisectors}\:{of}\:{a}\:{cyclic}\: \\ $$$${quadrilateral}\:{is}\:{also}\:{cyclic}. \\ $$ Answered by mrW1 last updated on 22/Feb/17 $${ABCD}\:{is}\:{a}\:{convex}\:\:{quadrilateral}. \\…
Question Number 76203 by Master last updated on 25/Dec/19 Commented by Master last updated on 25/Dec/19 $$\mathrm{example}: \\ $$$$\sqrt[{\mathrm{3}}]{−\mathrm{8}}=? \\ $$$$\left(−\mathrm{8}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} =? \\ $$ Commented…
Question Number 76200 by Joel578 last updated on 25/Dec/19 Commented by benjo last updated on 25/Dec/19 $$\mathrm{thanks}\:\mathrm{sir}.\:\mathrm{merry}\:\mathrm{chrismastto}\:\mathrm{all} \\ $$ Commented by Rio Michael last updated…
Question Number 10665 by FilupS last updated on 22/Feb/17 $${n}\mathrm{th}\:\mathrm{prime}\:=\:{p}_{{n}} \\ $$$${n}\mathrm{th}\:\mathrm{non}−\mathrm{prime}\:=\:{q}_{{n}} \\ $$$$\: \\ $$$$\mathrm{Determine}\:\mathrm{if}\:{q}_{{n}} >{p}_{{n}} \:\mathrm{for}\:\forall{n}\geqslant\mathrm{2} \\ $$ Commented by FilupS last updated…
Question Number 10664 by FilupS last updated on 22/Feb/17 $${S}=\underset{\underset{{n}\geqslant\mathrm{1}} {{n}\notin\mathbb{P}}} {\overset{\infty} {\sum}}{n} \\ $$$${Q}=\underset{\underset{{n}\geqslant\mathrm{1}} {{n}\in\mathbb{P}}} {\overset{\infty} {\sum}}{n} \\ $$$$\: \\ $$$$\mathrm{Prove}\:\mathrm{if}\:\mathrm{true}: \\ $$$${S}>{Q} \\…
Question Number 141733 by BHOOPENDRA last updated on 23/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10662 by FilupS last updated on 22/Feb/17 $$\mathrm{determine}\:\mathrm{if}: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{s}} }+\frac{\mathrm{1}}{\mathrm{3}^{{s}} }+\frac{\mathrm{1}}{\mathrm{5}^{{s}} }+…\geqslant\frac{\mathrm{1}}{\mathrm{1}^{{s}} }+\frac{\mathrm{1}}{\mathrm{4}^{{s}} }+\frac{\mathrm{1}}{\mathrm{6}^{{s}} }+… \\ $$$$\mathrm{or}: \\ $$$$\underset{\underset{{n}\geqslant\mathrm{1}} {{n}\in\mathbb{P}}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{s}}…