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Math Help - determine whether the following series converge or diverge

  1. #1
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    determine whether the following series converge or diverge

    Determine whether the following series converge or diverge:


    (3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

    5^n/n!. Converges by ratio test

    1/l(og(n))^n converges by ratio test

    (-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0


    I'm a bit suspicious of my answers since I got that they all converge

    Thanks in advance
    Last edited by mr fantastic; May 14th 2011 at 05:43 AM. Reason: Copied title into main body of post.
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by poirot View Post
    I'm a bit suspicious of my answers since I got that they all converge

    (3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

    5^n/n!. Converges by ratio test

    1/l(og(n))^n converges by ratio test

    (-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0

    Thanks in advance
    if a_n \rightarrow a and b_n \rightarrow b with b_n,b \neq 0 for all n then \frac{a_n}{b_n} \rightarrow \frac{a}{b}.
    define a_n=\frac{3}{n^2}+\frac{6}{n^4}-\frac{17}{n^6}, \, b_n=2-\frac{9}{n^2} + \frac{1}{n^5} +\frac{1}{n^6}. then a_n \rightarrow 0, \, b_n \rightarrow 2. also b_n \neq 0. so \frac{a_n}{b_n} \rightarrow 0

    now \frac{a_n}{b_n}= \frac{3n^4+6n^2-17}{2n^6-9n^4+n+1}
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  3. #3
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    They are series not sequences and I just need to tell whether they converge or diverge. Thanks anyway.
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    Quote Originally Posted by poirot View Post
    Determine whether the following series converge or diverge:


    (3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

    use the limit comparison test with the known convergent series 1/n^2

    5^n/n!. Converges by ratio test

    correct

    1/l(og(n))^n converges by ratio test

    correct, but try root test

    (-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0

    correct
    ...
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  5. #5
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    Thanks for suggesting the root test. It reminds me of the ratio test in that if c<1 it converges. Anyway so I was correct they are converge?
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