Determine whether the series is convergent or divergent

  • Thread starter Hypnos_16
  • Start date
  • #1
153
1

Homework Statement



I have to find whether the following is Convergent or Divergent

∑ from n = 1 to infinity
2 / n(2n + 2)^(1/4)

Actually it's the fourth root, this is just easier to write.

Homework Equations



According to the front of the sheet it's a quiz on P-Series and Integral Test
I'm leaning more towards Integral Test.

The Attempt at a Solution



Not sure how to go about it, i think i've been looking at them for too long, i can't seem to remember how to do integrals anymore
 

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,998
1,573
I wouldn't use the integral test.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
963
Either one will work. The "P-series" test says that a series of the form [itex]\sum n^p[/itex] will converge if p< 1, diverge if [itex]p\ge 1[/itex]. This is not exactly of that form, but you can use the comparison test also. Can you find a p so that [itex]1/(n(2n+2)^{1/4}< n^p[/itex]? The integral test says that a series [itex]\sum a_n[/itex] converges if the integral [itex]\int_1^\infty a(x)dx[/itex] converges where "a(x)" is just [itex]a_n[/itex] with "n" replaced by "x". Can you integrate
[tex]\int_1^\infty \frac{1}{x(x+1)}dx[/tex]?
 

Related Threads on Determine whether the series is convergent or divergent

Replies
3
Views
393
Replies
11
Views
9K
Replies
1
Views
3K
Replies
2
Views
5K
Replies
2
Views
637
Replies
15
Views
6K
Replies
1
Views
1K
Replies
3
Views
4K
Replies
2
Views
2K
Top