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Math Help - help with sum for absolute convergence

  1. #1
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    help with sum for absolute convergence

    SUM n_infinity (-1)^n+1 (3n/n!)

    I believe this is solved using the absolute ratio test.

    I see where this becomes lim n -> infinity (3n+1)/(n+1)! / 3n/n!

    =

    lim n->infinity 3/(n +1) = 0

    Is it common for this series to always divide by the original equation? what happened to the (-1)^n+1

    i need some help understanding whats going on.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rcmango View Post
    SUM n_infinity (-1)^n+1 (3n/n!)

    I believe this is solved using the absolute ratio test.

    I see where this becomes lim n -> infinity (3n+1)/(n+1)! / 3n/n!

    =

    lim n->infinity 3/(n +1) = 0

    Is it common for this series to always divide by the original equation? what happened to the (-1)^n+1

    i need some help understanding whats going on.
    you are incorrect with the first part.

    it's (3(n+1))/(n+1)! / 3n/n! not (3n+1)/(n+1)! / 3n/n! you forgot the brackets around n+1, that makes the answer totally different. in fact, it makes the solution unknown by the ratio test, since using the ratio test will give a limit of 1.

    the (-1)^n+1 doesn't matter since you took absolute values when doing the test, so you assume it is always positive.

    use the alternating series test here
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  3. #3
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    okay, your saying to use the alternating series to prove its convergent with this part: (-1)^n+1

    thus being always positive?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rcmango View Post
    okay, your saying to use the alternating series to prove its convergent with this part: (-1)^n+1

    thus being always positive?
    hmm, i don't really get your question. do you know what the alternating series test is? you pretty much forget about the (-1)^(n+1).

    once the terms are strictly decreasing (that is if we treat them as all positive) and the limit of the expression goes to zero as n goes to infinity, then it is absolutely convergent by the alternating series test. and if a series is absolutely convergent, then it's convergent
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  5. #5
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    ya, i see now. I was confused by the part were supposed to ignore.

    thanks for the help.
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