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Math Help - series and sequences

  1. #1
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    series and sequences

    let an=2n/(3n^2+2)
    a.)determine whether the sequence {an}n=1-infinity is convergent or divergent. If it converges find the limit
    b.)determine whether the series sum from n=1 to infinity of an is convergent or divergent.

    Can someone explain to me how to do this i am completely confused on series and apparently this is an easy workout problem. Help please? Thanks!
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  2. #2
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    Quote Originally Posted by ahawk1 View Post
    let an=2n/(3n^2+2)
    a.)determine whether the sequence {an}n=1-infinity is convergent or divergent. If it converges find the limit
    b.)determine whether the series sum from n=1 to infinity of an is convergent or divergent.

    Can someone explain to me how to do this i am completely confused on series and apparently this is an easy workout problem. Help please? Thanks!

    A sequence converges if it has a limit as n->infinity, and diverges if the limit DNE or is infinity.

    start with that. try it and see what you get
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  3. #3
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    Quote Originally Posted by coolguy99 View Post
    A sequence converges if it has a limit as n->infinity, and diverges if the limit DNE or is infinity.

    start with that. try it and see what you get
    it goes to 0 if u take the limit so it converges.
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  4. #4
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    For the limit of the series, note that 4n^2 > 3n^2 + 2 for n \geq 2. Hence, \frac{2n}{3n^2 + 2} > \frac{2n}{4n^2} for n \geq 2. But \frac{2n}{4n^2} = \frac{1}{2n} which is a multiple of the harmonic series. What can you conclude from this?
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