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Math Help - sequences

  1. #1
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    sequences

    how does one tell if an= 2n/(3n+1) is convergent?

    i think i remember my instructor saying that you can't just use the coefficients of the highest degrees of n.. but i missed this lesson

    also, upon deciding whether or not that is convergent, how do you decide if the series from n=1 to infinity is convergent?
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  2. #2
    o_O
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    For sequences, if \lim_{n \to \infty} a_n exists, then it is convergent.

    For series, there are a lot of tests that you can use to determine whether or not \sum a_n is convergent.

    For this particular example, we have the divergent test which says: If \lim_{n \to \infty} a_n \neq 0, then \sum a_n is divergent.
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