Comparison Test

  • Thread starter ProBasket
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  • #1
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Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test.

[tex]\sum_{n=1}^\infty \frac{2n^4}{n^5+7}[/tex] this diverges using the p-series and comparison test right? p <1


[tex]\sum_{n=1}^\infty \frac{2n^4}{n^9+7}[/tex] and this converges right? because p > 1



[tex]\sum_{n=1}^\infty \frac{-1^n}{9n}[/tex] i think this also diverges cause p <1. (not sure about this one)

can someone check these real quick and tell me if im correct?
 

Answers and Replies

  • #2
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First one, P = 1, it diverges.

2 is correct.

Hint for the last one

[tex] \sum_{n=1}^{\infty} - \frac{1^n}{9n} [/tex]

Whats [itex] 1^n [/itex] for positive n? It should be easy after that.
 
  • #3
HallsofIvy
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I suspect he meant [tex] \sum_{n=1}^{\infty} -\frac{(-1)^n}{9n} [/tex] for the last one. That converges because it is an alternating series with terms going to 0.
 
  • #4
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I was going to make that suggestion, but since his post mentions the comparison test, I decided that the way he originally posted was likely the way that he meant it (since the comparison test can't be used for conditionally convergent series).
 

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