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KonradZuse

  • 3 years ago

Alternating series Q:

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  1. KonradZuse
    • 3 years ago
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    In the book there is an example that's \[\sum_{n=1}^{\infty} \frac{n}{(-2)^{n-1}}\]

  2. vf321
    • 3 years ago
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    Well if n->infinity, then n/(n+1) is 1 since n goes to infinity at the same rate. We also know that the base case, n = 1, IS 1/2, and that the function's monotonic, so n/(n+1) HAS to be between 1/2 and 1...

  3. vf321
    • 3 years ago
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    Slight note: Monotonic over [1, infty]

  4. anonymous
    • 3 years ago
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    how or why? the how is clear right? if \(n>1\) then \(\frac{n+1}{n}>\frac{1}{2}\) for sure

  5. vf321
    • 3 years ago
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    Well that's a property of your book's proof. If you like, we can probably do an ALTERNATE one (get it?).

  6. vf321
    • 3 years ago
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    NVM. The point is, whatever your book is doing to prove the alternating series converges, it needs that fact...

  7. vf321
    • 3 years ago
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    Well do you have to make a formal proof? Or an AP Calc BC-suitable proof?

  8. KonradZuse
    • 3 years ago
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  9. KonradZuse
    • 3 years ago
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    Do we have to do stuff like this, or just apply the rules in the theorm to see if it wortks or not?

  10. vf321
    • 3 years ago
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    lol it was ap calc bc. Nice guess on my part, huh? Yeah for AP you just say "this converges by ALT series test" because of the three conditions for alternating series. Do you know them?

  11. KonradZuse
    • 3 years ago
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    The course I'm in is Calc 2.

  12. KonradZuse
    • 3 years ago
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    The book only says 2 conditons an+1 < an and an = 0.

  13. KonradZuse
    • 3 years ago
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    I did the question I was goign to do and was correct, but I did do it a diff way than the professor..

  14. vf321
    • 3 years ago
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    Well in that case I can't guess your course needs... and the third condition is that the "non alternating part" has to be always positive.

  15. KonradZuse
    • 3 years ago
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    Seems like a lot of L'hospitals rule is used.. Should bone up.

  16. KonradZuse
    • 3 years ago
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    oh yeah it says let an > 0

  17. vf321
    • 3 years ago
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    LH is a good thing to always keep in your mind.

  18. KonradZuse
    • 3 years ago
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    so hmm... can you check out the first picture and see what they are doing?

  19. KonradZuse
    • 3 years ago
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    not sure if it's important for my needs.

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