Infinite Series

  • Thread starter Rossinole
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  • #1
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Homework Statement



Is the series from n=1 to infinity of 3/n converging or diverging?

Homework Equations




The Attempt at a Solution



Since 3/n is not a geometric series, my guess is that we can just use the Test for Divergence and take it's limit to see if it's converging or diverging. As n->infinity, 3/n -> 0 and lim = 0, so it's converging.

However, I am not sure if this is right way to go about it.
 

Answers and Replies

  • #2
Tom Mattson
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Since 3/n is not a geometric series,

Correct.

my guess is that we can just use the Test for Divergence and take it's limit to see if it's converging or diverging.

Not a bad guess, but beware that the Test for Divergence cannot tell you if a series converges (hence, its name).

As n->infinity, 3/n -> 0 and lim = 0, so it's converging.

Wrong. The Test for Divergence says that:

[tex]\lim_{n\rightarrow\infty}a_n \neq 0 \Rightarrow \sum_{n=1}^\infty a_n[/tex] diverges.

Equivalently, it says that:

[tex]\sum_{n=1}^\infty a_n[/tex] converges [tex]\Rightarrow \lim_{n\rightarrow\infty}a_n = 0[/tex]

If the limit is zero, then the test yields no information and you have to use another test.
 
  • #3
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So I would have to treat it as a Harmonic Series?
 
  • #4
Tom Mattson
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It is a harmonic series.
 
  • #5
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Alright, thank you for your help.
 

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