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Alternating series test

  1. Dec 9, 2011 #1
    Alternating series test:

    1. All the [tex]u_n[/tex] are all positive

    2. [tex]u_n\geq u_{n+1}[/tex] for all [tex]n \geq N[/tex]. For some integer N

    3. [tex]u_n \rightarrow 0[/tex]

    I thought it would hold with 2. and that the su m of the N first terms were not [tex]\infty[/tex]

    Here is the theroem just in case:


    Here they assume N=1 how can they do that?
  2. jcsd
  3. Dec 9, 2011 #2
    How can the sum of the first N terms ever equal infinity?? If you add up finitely many real number, then you never get infinity.

    The proof for arbitrary N is very similar. Try to prove it yourself!!
    (or even better: reduce to the case N=1)
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