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Convergent and Divergent problem

  1. Jan 24, 2008 #1
    If I have [tex] (a_n + b_n)^n = c_n [/tex] where a_n is convergent and b_n divergent. Is c_n then divergent?

    And what if a_n and b_n were divergent, would c_n be divergent also?

    but what if they were both convergent then surely c_n is convergent right?

    I can't see a rule or a theorem that tells me this is correct and frankly it is getting on my nerve.

    Somebody here who knows? :smile:

  2. jcsd
  3. Jan 24, 2008 #2
    Hve u tried an epsylon- delta proof? I think it might work.
  4. Jan 24, 2008 #3


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    No conclusion is possible for the convergence of [itex]c_n[/itex].

    [tex]a_n=0, b_n=(-1)^n \times \frac{1}{4}[/tex]
    [tex]a_n=1, b_n=(-1)^n[/tex]
    [tex]a_n=b_n=(-1)^n [/tex]
    [tex]a_n=b_n=(-1)^n \times \frac{1}{4}[/tex]
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