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privetek Group Title

determine absolute or conditional convergence: sum(k=1 -> infinity) [(-1)^(k+1)(10^k)]/(k!)

  • one year ago
  • one year ago

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  1. mukushla Group Title
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    have u tried ratio test?

    • one year ago
  2. privetek Group Title
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    well it's an alternating series. i think i'm supposed to use the alternating series test

    • one year ago
  3. mukushla Group Title
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    of course alternating series test will work :)

    • one year ago
  4. privetek Group Title
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    i'm not sure how i'm supposed to do it because of the k+1 on the -1

    • one year ago
  5. mukushla Group Title
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    u just need to drop \[(-1)^{k+1}\]and then work on\[\frac{10^k}{k!}\]

    • one year ago
  6. mukushla Group Title
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    this is a good sourse http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

    • one year ago
  7. mukushla Group Title
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    what is ur difficulty with that??

    • one year ago
  8. privetek Group Title
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    ok.. now i get that.. so how should i take the limit of 10^k/k! ?

    • one year ago
  9. mukushla Group Title
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    oh sorry i was out ;) well k! is very greater than 10^k when k increses

    • one year ago
  10. mukushla Group Title
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    *increases

    • one year ago
  11. privetek Group Title
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    so would that mean that the limit would go to zero?

    • one year ago
  12. mukushla Group Title
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    yes

    • one year ago
  13. privetek Group Title
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    how to tell weather it converges absolutely or conditionally?

    • one year ago
  14. mukushla Group Title
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    emm...u should apply Absolute Convergence test

    • one year ago
  15. privetek Group Title
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    sorry.. i kinda don't understand how to do that here... could you help me out??

    • one year ago
  16. mukushla Group Title
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    ok u got the first part right? alternating series test?

    • one year ago
  17. privetek Group Title
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    yes, lim(k>infinity)[10^k/k!] = 0

    • one year ago
  18. privetek Group Title
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    therefore it converges

    • one year ago
  19. privetek Group Title
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    @mukushla

    • one year ago
  20. malevolence19 Group Title
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    \[\lim_{k \rightarrow \infty}a_k=0\] Is a REQUIREMENT for a series to converge but it doesn't not IMPLY that a series converges.

    • one year ago
  21. malevolence19 Group Title
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    it does not*

    • one year ago
  22. malevolence19 Group Title
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    Even if it is an alternating series do the ratio test, the ratio test works well for factorials. Also, if that converges then you know it absolutely converges (because you take the absolute value so the (-1)^k+1 goes away) and if it absolutely converges then you know it conditionally converges.

    • one year ago
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