# Now f is positive and decreasing on 1 in addition i t

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Nowfis positive and decreasing on (1,);in addition,integraldisplayt4f(x)dx=bracketleftbigg1(lnx)3bracketrightbiggt4=1(ln 4)31(lnt)3,
trevino ochoa (dt23653) – HW13 – mostovyi – (54020)10in which case,integraldisplay4f(x)dx=limt→ ∞integraldisplayt4f(x)dx=limtbraceleftBig1(ln 4)31(lnt)3bracerightBig=1(ln 4)summationdisplayn=2vextendsinglevextendsinglevextendsinglevextendsingle(1)nnn2+ 2vextendsinglevextendsinglevextendsinglevextendsingle=summationdisplayn=2nn2+ 2.
→ ∞3.Consequently, by the Integral Test, the givenseriesconverges.01610.0pointsWhich one of the following properties doesthe seriessummationdisplayn=2(1)nnn2+ 2have?But this last series diverges by thep-seriesand Limit Comparison Tests. Consequently,the seriessummationdisplayn=2(1)nnn2+ 2isconditionally convergent.01710.0pointsDetermine whether the seriessummationdisplayn=12(n)3nis absolutely convergent, conditionally con-vergent or divergent
converges. Does it converge absolutely? Well,summationdisplayn=2vextendsinglevextendsinglevextendsinglevextendsingle(1)nnn2+ 2vextendsinglevextendsinglevextendsinglevextendsingle=summationdisplayn=2nn2+ 2.
Which of the following series converge?A.summationdisplayk=1parenleftbigg4k3k+ 1parenrightbiggkB.summationdisplayk=21klnk+ 5kSince11 +5lnk−→1>0ask→ ∞, the limit comparison test applies.On the other hand, by the Integral Test theseriessummationdisplayk=21klnkdiverges. Consequently, the seriessummationdisplayk=21klnk+ 5kdoes not converge.01910.0pointsDetermine whether the series4859+610711+812. . .summationdisplayk=21klnk+ 5kdoes not converge.01910.0pointsDetermine whether the series4859+610711+812. . .