• Support PF! Buy your school textbooks, materials and every day products Here!

Absolute & conditional convergence

  • Thread starter magnifik
  • Start date
  • #1
360
0

Homework Statement


Determine whether the series converges absolutely, conditionally, or not at all.

a) [tex]\Sigma[/tex] (-1)nn4/(x3 + 1)

b) [tex]\Sigma[/tex] sin(x)/x2


Homework Equations





The Attempt at a Solution


a) positive series is n4/n3+1 .. do i do comparison test ??

b) |sin(x)|/x2
compare it with 1/x2 which converges.. so it's absolutely convergent??
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
You are kind of freely mixing n's and x's here. Are they supposed to be the same? If so, for the first one ask whether the nth term goes to zero. For the second one, yes, it's absolutely convergent.
 
  • #3
360
0
woops, mixing up the n's & x's was a careless mistake
 
  • #4
360
0
for a) the positive series diverges because n^4/n^3 + 1 goes to infinity, but i'm not sure if the original series converges or diverges
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
618
for a) the positive series diverges because n^4/n^3 + 1 goes to infinity, but i'm not sure if the original series converges or diverges
A series whose terms don't go to zero diverges no matter what the signs on the terms. Look at the definition of convergence in terms of partial sums.
 

Related Threads on Absolute & conditional convergence

Replies
6
Views
1K
Replies
4
Views
2K
Replies
4
Views
2K
Replies
2
Views
2K
Replies
6
Views
3K
Replies
7
Views
2K
Replies
6
Views
3K
Replies
2
Views
791
Replies
1
Views
831
Top