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privetek

  • 2 years ago

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

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  1. mukushla
    • 2 years ago
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    have u tried ratio test?

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

  3. mukushla
    • 2 years ago
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    of course alternating series test will work :)

  4. privetek
    • 2 years ago
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    i'm not sure how i'm supposed to do it because of the k+1 on the -1

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

  6. mukushla
    • 2 years ago
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    this is a good sourse http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

  7. mukushla
    • 2 years ago
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    what is ur difficulty with that??

  8. privetek
    • 2 years ago
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    ok.. now i get that.. so how should i take the limit of 10^k/k! ?

  9. mukushla
    • 2 years ago
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    oh sorry i was out ;) well k! is very greater than 10^k when k increses

  10. mukushla
    • 2 years ago
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    *increases

  11. privetek
    • 2 years ago
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    so would that mean that the limit would go to zero?

  12. mukushla
    • 2 years ago
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    yes

  13. privetek
    • 2 years ago
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    how to tell weather it converges absolutely or conditionally?

  14. mukushla
    • 2 years ago
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    emm...u should apply Absolute Convergence test

  15. privetek
    • 2 years ago
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    sorry.. i kinda don't understand how to do that here... could you help me out??

  16. mukushla
    • 2 years ago
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    ok u got the first part right? alternating series test?

  17. privetek
    • 2 years ago
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    yes, lim(k>infinity)[10^k/k!] = 0

  18. privetek
    • 2 years ago
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    therefore it converges

  19. privetek
    • 2 years ago
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    @mukushla

  20. malevolence19
    • 2 years ago
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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.

  21. malevolence19
    • 2 years ago
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    it does not*

  22. malevolence19
    • 2 years ago
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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.

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