okevino Messages 13 Reaction score 0 Thread starter Apr 24, 2007 #1 see attachment thanks. Attachments convergence2.JPG 10 KB · Views: 413
quasar987 Science Advisor Homework Helper Gold Member Messages 4,796 Reaction score 32 Apr 24, 2007 #2 That a_n-->0 in [tex]\sum a_n[/tex] does not imply that the series is convergent. You should re-read that theorem in your notes/book more carefully to see what it's actually saying.
That a_n-->0 in [tex]\sum a_n[/tex] does not imply that the series is convergent. You should re-read that theorem in your notes/book more carefully to see what it's actually saying.
HallsofIvy Science Advisor Homework Helper Messages 42,895 Reaction score 983 Apr 24, 2007 #3 lim an= 0 is a necessary condition that [tex]\Sigma a_n[/tex] converge, not a sufficient condition! The first one "compares" to the sum of 1/n which does NOT converge.
lim an= 0 is a necessary condition that [tex]\Sigma a_n[/tex] converge, not a sufficient condition! The first one "compares" to the sum of 1/n which does NOT converge.