# On the other hand lim x 1 x lnx 0 consequently by the

• Notes
• 13
• 100% (3) 3 out of 3 people found this document helpful

This preview shows page 11 - 13 out of 13 pages.

On the other hand,limx→ ∞1xlnx= 0.Consequently, by the Alternating series Test,the given series isconditionally convergent.01810.0pointskdoes not converge.B. We use the limit comparison test, com-paring the given seriessummationdisplayk=21klnk+ 4kwith the seriessummationdisplayk=21klnk.Nowklnkparenleftbigg1klnk+ 4kparenrightbigg=11 +4lnk.Since11 +4lnk−→1>0
Which of the following series converge?
Explanation:Which, if any, of the following statements aretrue?The Ratio Test can be used to deter-mine whether the seriessummationdisplayn=1/n!converges or diverges.B. The Root Test can be used to determinewhether the seriessummationdisplayk=1k3 +k2parenrightBigkdoes not converge.B. We use the limit comparison test, com-paring the given seriessummationdisplayk=21klnk+ 4kwith the seriessummationdisplayk=21klnk.Nowklnkparenleftbigg1klnk+ 4kparenrightbigg=11 +4lnk.Since11 +4lnk−→1>0
A.The Ratio Test can be used to deter-mine whether the seriessummationdisplayn=1/n!converges or diverges.B. The Root Test can be used to determinewhether the seriessummationdisplayk=1k3 +k2
hemyari (kh27237) – HW13 – ben-zvi – (54740)12converges or diverges.Consequently,limn→ ∞vextendsinglevextendsinglevextendsinglean+1anvextendsinglevextendsinglevextendsingle= 0,and so by the Ratio Test, the given seriesconverges.