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Thread: Sequences and Series

  1. #1
    Sep 2008

    Sequences and Series

    Hey I'm in my 2nd year of calculus and we no longer do sequences and series, I had a friend of mine ask me about a question he had, and tried to work out and ended up not getting it completely and handing it in partially completed for some marks, he got me thinking and these are the two questions he had trouble with, can anyone shed some light on them for me to relay back to him. Thanks.

    Determine if the sequence is convergent or divergent, if convergent what does it converge to?

    $\displaystyle \{\frac{(\ln (n))^3}{n^2}\}$ $\displaystyle \{(3(n^2) + 1)^(2/n)\}$

    Those are the two questions he asked me about, thanks!
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  2. #2
    Junior Member
    Mar 2009
    A sequence converges if the lim (as n-> infinity exists), and diverges if the lim is infinity, or DNE

    also, tell him that when taking limits, if he happens to get 0/0, or infinity/infinity, he can do L'Hopital's rule to find the real limit (and also that, if he tries to find the limit and comes up with infinity times infinity, or 0 times 0, he can re-work them algebraically to be inf/inf, or 0/0. an example of this would be (x)ln(1 +1/x). normally this would be infinity times 0, but reworking it... ln(1 +1/x)/(1/x) = 0/0, and do L'Hopitals from there).
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