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Series with two variables

  1. Nov 18, 2012 #1
    Examine for which [itex] u \in \mathbb R [/itex] the series [itex]\sum\limits_{n=1}^\infty \frac {(1+(-1)^n)^n}{n^2} |u|^{\sqrt{n}(\sqrt{n+1})} [/itex]
    converges.

    What I found out so far: [itex](1+(-1)^n)[/itex] alternates between [0;2], that means that the whole series becomes zero for the even [itex]n[/itex]. The interesting part are the odd [itex]n[/itex] but what role plays [itex]u[/itex]. I´m still a bit confused with the roots in the exponent of [itex]u[/itex]

    Thanks....;)
     
  2. jcsd
  3. Nov 18, 2012 #2

    haruspex

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    You mean, the even n terms vanish, right? That being so, can you rewrite the series in a simpler form, preferably in a way that has all terms positive? Then, what tests do you know for convergence of series?
     
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