Question Number 3061 by Rasheed Soomro last updated on 04/Dec/15 $$\mathrm{Determine}\:\:\mathrm{nth}\:\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$\mathrm{1},\mathrm{0},−\mathrm{1},\mathrm{0},\mathrm{7},\mathrm{28},\mathrm{79},… \\ $$ Commented by prakash jain last updated on 04/Dec/15 $${one}\:{techinque}\:{is}\:{to}\:{define} \\…
Question Number 3027 by Rasheed Soomro last updated on 03/Dec/15 $${Determine} \\ $$$$\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{3}} +… \\ $$ Commented by Filup last updated on 03/Dec/15 $$=\underset{{i}=\mathrm{1}}…
Question Number 3022 by Rasheed Soomro last updated on 03/Dec/15 $$\mathrm{Determine} \\ $$$$\mathrm{1}+\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{3}}} +… \\ $$ Commented by prakash jain last updated on 04/Dec/15…
Question Number 68549 by gunawan last updated on 13/Sep/19 $${y}=\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${y}^{−\mathrm{1}} =… \\ $$ Commented by mathmax by abdo last updated on…
Question Number 3003 by Rasheed Soomro last updated on 02/Dec/15 $${What}\:{is}\:{nth}\:{term}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{5}}{\mathrm{4}},\frac{\mathrm{15}}{\mathrm{8}},\frac{\mathrm{37}}{\mathrm{16}},\frac{\mathrm{83}}{\mathrm{32}}… \\ $$ Commented by Rasheed Soomro last updated on 05/Dec/15 $$\underset{−} {\mathcal{HIGH}{ly}}\:\mathcal{A}{ppriciate}\:\mathcal{Y}{our}\:\overset{\mathcal{VALUEABLE}}…
Question Number 134067 by bramlexs22 last updated on 27/Feb/21 $$\:\mathrm{Calculate}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{n}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{3}} −\mathrm{1}}{\mathrm{k}^{\mathrm{3}} +\mathrm{1}}\:=\:? \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\:{since}\:\frac{{k}^{\mathrm{3}}…
Question Number 134060 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{If}\:\mathrm{p}>\mathrm{1}\:\mathrm{and}\:\mathrm{q}>\mathrm{1}\:\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\mathrm{the}\:\mathrm{convergence}\: \\ $$$$\mathrm{of}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{p}} .\left(\mathrm{ln}\:\mathrm{n}\right)^{\mathrm{q}} }\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges} \\…
Question Number 134061 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{If}\:\Sigma\:\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{convergent}\:\mathrm{series}\:\mathrm{of} \\ $$$$\mathrm{nonnegative}\:\mathrm{terms},\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\Sigma\:\mathrm{a}_{\mathrm{n}} .\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverge} \\ $$…
Question Number 134052 by shaker last updated on 27/Feb/21 Answered by mathmax by abdo last updated on 27/Feb/21 $$\mathrm{I}\:=\int\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\mathrm{3}}\mathrm{dx}\:\:\Rightarrow\mathrm{I}\:=\int\:\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\left(\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{6}}} \right)^{\mathrm{6}} }\mathrm{dx}\:=_{\mathrm{x}=\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{6}}}…
Question Number 2980 by Filup last updated on 02/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\frac{{d}}{{dx}}\left({e}^{{x}} \right)={e}^{{x}} \\ $$$$\mathrm{Assume}\:\mathrm{that}\:\mathrm{you}\:\mathrm{do}\:\mathrm{not}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{above}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{true}. \\ $$ Answered by RasheedAhmad last updated on 02/Dec/15 $${e}^{{x}}…