3 true or false

  • Thread starter Spruance
  • Start date
  • #1
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True or false, justify your answer

1) If [tex]\sum_{n=1}^\infty a_n[/tex] converges, then [tex]\sum_{n=1}^\infty (-1)^n \ a_n[/tex] converges.

2) If [tex]\sum_{n=1}^\infty a_n[/tex] converges and [tex]\sum_{n=1}^\infty (-1)^n \ a_n[/tex] converges, then [tex]\sum_{n=1}^\infty a_n[/tex] converges absolutely.

3) If [tex]\sum_{n=1}^\infty a_n[/tex] converges absolutely, then [tex]\sum_{n=1}^\infty (-1)^n \ a_n[/tex] converges absolutely.

Can anybody help me with this one?

Thanks in advance
 
Last edited:

Answers and Replies

  • #2
Hootenanny
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your [t e x] tags must be in lower case.

~H
 
  • #3
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Thank you, Hootenanny. That fixed everything!
 
  • #4
Hootenanny
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RE: Your question, what are the criteria for absolute convergence?

~H
 
  • #5
HallsofIvy
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Or, what is the definition of "absolute convergence"?
 

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