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Given 2 series' an bn, what can be said about cn when

  1. Apr 10, 2009 #1
    given 2 unknown number series {an}[tex]^{infinity}_{n=1}[/tex] and {bn}[tex]^{infinity}_{n=1}[/tex], if it is know that {an}[tex]^{infinity}_{n=1}[/tex]=infinity and {bn}[tex]^{infinity}_{n=1}[/tex]=K,
    K=constant unknown

    what can be said about
    {an+bn}[tex]^{infinity}_{n=1}[/tex]
    {an*bn}[tex]^{infinity}_{n=1}[/tex]


    i think that
    {an+bn}[tex]^{infinity}_{n=1}[/tex]= infinity, since:
    {an+bn}[tex]^{infinity}_{n=1}[/tex]={an}[tex]^{infinity}_{n=1}[/tex]+{bn}[tex]^{infinity}_{n=1}[/tex]= infinity + K = infinity

    as for {an*bn}[tex]^{infinity}_{n=1}[/tex], i dont think anything can be said for sure, since K could be a number or 0,

    am i right?? is there a proper mathematical way to write this?
     
  2. jcsd
  3. Apr 10, 2009 #2

    MathematicalPhysicist

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    Gold Member

    Partially right.
    If K=0 it's usually undefined, but if K>0 then K*infinity=infinity and if K<0 then... what can you say it equals to?

    If you need to check the definitions there they are:
    1. a_n=infinity iff for every M>0 there exists N such that for every n>N a_n>M
    2. a_n=-infinity iff for every M<0 there exists N such that for every n>N a_n<M.
     
  4. Apr 10, 2009 #3
    i am asked is Cn converges when
    Cn=An+Bn,---> does not converge

    Cn=AnBn--->if |Bn|>0 - does not converge
    but if Bn=0, then it is undefined, so what does that mean, diverge/converge/something else??
     
  5. Apr 10, 2009 #4

    MathematicalPhysicist

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    Gold Member

    Well, now when I think of it if Bn=0, and An->infinity then AnBn->0 because AnBn=0 for every natural n.
    If the question were, Bn->0 but not indetically 0, then it's undefined.
     
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