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anonymous

  • 5 years ago

I am trying to determine if the following is absolutely or conditionally convergent or divergent....

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  1. anonymous
    • 5 years ago
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    \[\sum_{n=1}^{\infty} (\sin 4n / 4^{n})\]

  2. anonymous
    • 5 years ago
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    Ok. We can treat sin(4n) as (-1)^n. This is because the sine function varies between -1 and 1.

  3. anonymous
    • 5 years ago
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    So that would give us [(-1)^n]/4^n. What kind of series does that look like?

  4. anonymous
    • 5 years ago
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    so use the alternating series test?

  5. anonymous
    • 5 years ago
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    Yes :)

  6. anonymous
    • 5 years ago
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    ok, for some reason I thought I could only do that with cos

  7. anonymous
    • 5 years ago
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    I don't know why

  8. anonymous
    • 5 years ago
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    Nope works for both. Don't worry I get hiccups like that all the time. :)

  9. anonymous
    • 5 years ago
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    thanks, pops!

  10. anonymous
    • 5 years ago
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    you just helped me too pops I am doing an assignment on that as we speak

  11. anonymous
    • 5 years ago
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    Your welcome :)

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spraguer (Moderator)
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