Does the Series Converge or Diverge?

  • #1

Homework Statement


Determine whether the infinite series converges or divergens. If it converges find its sum.
[itex] \sum^{∞}_{k=1} \frac{k-3}{k}[/itex]


Homework Equations





The Attempt at a Solution



I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.


However, I'm not sure if I'm using the test for divergence right.
 

Answers and Replies

  • #2
111
0


I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.



You are contradicting yourself. Do you think it converges or diverges ?

Hint: This series doesn't converge try and use a comparison test too see why.
 
  • #3
You are contradicting yourself. Do you think it converges or diverges ?

Hint: This series doesn't converge try and use a comparison test too see why.

Sorry, I ment to say that the series diverges by the test for divergence because the limit is not equal to 0.
 
  • #4
111
0
Yes, by the non null test is this is divergent as the limit is not equal to zero.
 

Related Threads on Does the Series Converge or Diverge?

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
7
Views
12K
  • Last Post
Replies
3
Views
2K
Replies
15
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
1
Views
509
Top