Nth term test & convergence

  • Thread starter kuahji
  • Start date
  • #1
kuahji
394
2
For a problem such as [tex]\sum[/tex] (1-3/n)^n with the sum going from 1 to infinity, the textbook shows to use the nth term test & that it diverges. However in a previous chapter the textbook had a theorem that said the limit of [tex]\sum[/tex] (1+x/n)^n will converge to e^x for any number x.

So I'm confused. Are they using convergence in a different context or what am I missing?
 

Answers and Replies

  • #2
quasar987
Science Advisor
Homework Helper
Gold Member
4,793
21
It is (1+x/n)^n that converges to e^x, not the sum of that.

And actually, you can use this fact to show that the series in your problem diverges. You know that (1-3/n)^n converges to e^{-3}, which is not 0, hence the series diverges.
 
Last edited:
  • #3
kuahji
394
2
Thanks for the reply. I see that I obviously got confused ^_^.
 

Suggested for: Nth term test & convergence

Replies
1
Views
416
  • Last Post
Replies
4
Views
575
Replies
8
Views
235
  • Last Post
Replies
10
Views
314
Replies
3
Views
3K
  • Last Post
Replies
15
Views
802
  • Last Post
Replies
2
Views
327
  • Last Post
Replies
4
Views
533
Top