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anonymous

  • 5 years ago

Absolute Conversion... Sum(-1)^n/(5+n) Which test do I use?

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  1. anonymous
    • 5 years ago
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    \[\sum_{n=1}^{\infty} (-1)^{n}/(5+n)\]

  2. anonymous
    • 5 years ago
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    (-1)^n / n+5

  3. anonymous
    • 5 years ago
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    hey, how's it going?

  4. anonymous
    • 5 years ago
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    I think I got it... I just forgot that I should use the conversion rules: Bn+1 < Bn and lim (n->inf) =0

  5. anonymous
    • 5 years ago
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    the conversion rules? hmm, so what'd you get as the answer?

  6. anonymous
    • 5 years ago
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    well, I got conditionally convergent. But it seems that that isnt quite right. Could you go through the steps for me?

  7. anonymous
    • 5 years ago
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    first of all don't confuse conversion and convergence i assume it's convergence you've been talking about the whole time, right?

  8. anonymous
    • 5 years ago
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    hahaha, yeah oops.

  9. anonymous
    • 5 years ago
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    absolute convergence means that the absolute value converges. so you can deal with the series 1/(5+n)

  10. anonymous
    • 5 years ago
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    did you do any tests?

  11. anonymous
    • 5 years ago
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    I did ordinary convergence test. But that doesnt work. because I compared to 1/n, and that's divergent, but 1/n+5 is smaller than that.

  12. anonymous
    • 5 years ago
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    do you know the ratio test, the root test, and the integral test?

  13. anonymous
    • 5 years ago
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    yeah, but I have trouble deciding which to use.

  14. anonymous
    • 5 years ago
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    well you just have to start trying things, don't be lazy

  15. anonymous
    • 5 years ago
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    The issue is that when one test tells me that it's convergent, another tells me it's absolute convergent and another says divergent, I get confused. Since a function can be partially convergent etc. I need to sort out which test test what.

  16. anonymous
    • 5 years ago
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    well, you've made a mistake if the tests are telling you different things :)

  17. anonymous
    • 5 years ago
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    OCT, LCT, Integral, Ratio, Root, Absolute convergence By the way, the convergence rules I was talking about was the alternating series estimation theorem Which do I use first? My process right now is to use the theorem first. then if it's convergent, use one of the above. And for non alternating, just use one of the above what do you say? is there a better way?

  18. anonymous
    • 5 years ago
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    i don't know, it doesn't matter that much what order, just start doing tests. do you just have to find out if the series is absolutely convergent?

  19. anonymous
    • 5 years ago
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    Absolute convergent, conditionally convergent, or divergent is the exact wording

  20. anonymous
    • 5 years ago
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    ok, an alternating series converges if the limit of the last term approaches 0, and the series is monotonically decreasing which means that An >A(n+1)

  21. anonymous
    • 5 years ago
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    so if the terms are getting smaller, and the last term is going to 0, then it converges if it's an alternating series, so that part is not that hard

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