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S-n-0-n-2-n-1-n-3-does-S-converge-

Question Number 2497 by 123456 last updated on 21/Nov/15 $$\mathrm{S}=\underset{{n}=\mathrm{0}} {\overset{+\infty} {\sum}}\frac{{n}+\mathrm{2}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right)} \\ $$$$\mathrm{does}\:\mathrm{S}\:\mathrm{converge}? \\ $$ Answered by prakash jain last updated on 21/Nov/15 $$\mathrm{S}=\underset{{n}=\mathrm{0}}…

x-t-cos-t-y-t-sin-t-0-t-pi-If-z-f-x-y-is-a-curtain-with-height-of-1-what-is-the-surface-area-of-the-curtain-

Question Number 2491 by Filup last updated on 21/Nov/15 $${x}\left({t}\right)=\mathrm{cos}\:{t} \\ $$$${y}\left({t}\right)=\:\mathrm{sin}\:{t} \\ $$$$\mathrm{0}\leqslant{t}\leqslant\pi \\ $$$$ \\ $$$$\mathrm{If}:\:\:\:{z}={f}\left({x},\:{y}\right)\:\:\mathrm{is}\:\mathrm{a}\:'{curtain}'\:\mathrm{with}\:\mathrm{height}\: \\ $$$$\mathrm{of}\:\mathrm{1},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:'{curtain}'? \\ $$ Commented by Yozzi…

Evaluate-n-1-1-n-1-n-1-1-2-1-3-1-4-

Question Number 2489 by Filup last updated on 21/Nov/15 $$\mathrm{Evaluate}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\:\sqrt{{n}}}\right)=\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+… \\ $$ Commented by Yozzi last updated on 21/Nov/15 $$\underset{{r}=\mathrm{1}}…

2014-2013-2014-2013-2012-2011-2014-2013-2012-2011-2010-2009-2014-2013-2012-2011-2010-2009-2008-2007-4-3-2-1-

Question Number 2481 by Syaka last updated on 21/Nov/15 $$\frac{\mathrm{2014}}{\mathrm{2013}}\:+\:\frac{\mathrm{2014}}{\mathrm{2013}}\:\ast\frac{\mathrm{2012}}{\mathrm{2011}}\:+\:\frac{\mathrm{2014}}{\mathrm{2013}}\:\ast\:\frac{\mathrm{2012}}{\mathrm{2011}}\:\ast\:\frac{\mathrm{2010}}{\mathrm{2009}}\:+\:\centerdot\centerdot\centerdot\centerdot\:+\:\frac{\mathrm{2014}}{\mathrm{2013}}\:\ast\:\frac{\mathrm{2012}}{\mathrm{2011}}\:\ast\:\frac{\mathrm{2010}}{\mathrm{2009}}\:\ast\:\frac{\mathrm{2008}}{\mathrm{2007}\:}\ast\centerdot\centerdot\centerdot\ast\frac{\mathrm{4}}{\mathrm{3}}\ast\frac{\mathrm{2}}{\mathrm{1}}\:−\:\mathrm{1}\:=\:\:\:\:? \\ $$ Answered by Filup last updated on 21/Nov/15 $$\mathrm{if}\:\mathrm{by}\:''\ast''\:\mathrm{you}\:\mathrm{mean}\:''×'' \\ $$$${in}\:{form}\:\left({k}=\mathrm{2014}\right): \\ $$$$ \\…