Convergence/Divergence of this sequence

  • #1

Main Question or Discussion Point

Hello,

I am trying to find if this sequence is converging or diverging:

http://img9.imageshack.us/img9/623/72142860.gif [Broken]

Here is my work, but I highly doubt it because it is based on intuition:
http://img4.imageshack.us/img4/3589/54428513.gif [Broken]
Since the first limit diverges and the second limit is not equal to 0, then the sequence diverges.
Does anyone have a better, systematic way of dealing with this sequence and any other sign alternating sequence with (-1)^n

Thank you
 
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Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hello fishingspree2! :smile:
Hello,

I am trying to find if this sequence is converging or diverging:

http://img9.imageshack.us/img9/623/72142860.gif [Broken]
[/URL]

Do you mean the sum, ∑ of that?

Hint: try subtracting one term from the next … that'll give you a sum of positive terms. :wink:
 
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  • #4
tiny-tim
Science Advisor
Homework Helper
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oooh sorry :redface:

i was confused by the square brackets

(i wish the latex was back :frown:)

in that case …
Here is my work, but I highly doubt it because it is based on intuition:
http://img4.imageshack.us/img4/3589/54428513.gif [Broken]
Since the first limit diverges and the second limit is not equal to 0, then the sequence diverges.
Why do you doubt it … that's fine! :biggrin:

Just tune it slightly by saying that the even terms converge to 2, and the odd terms converge to -2, so clearly it has no limit. :smile:
 
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  • #5
thank you tiny-tim :)
 

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