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Homework Help: Proof help

  1. Oct 21, 2008 #1
    How do you prove ex * ey = ex + y using series?



    Prove:

    suppose sum an and sum bn converge absolutely then the series cn with cn = sum (from k=0 to n) ak*bn-k converges absolutely to the limit sum an * sum bn

    Thank you!

    Or if you have seen either of these on here could you redirect me to that page
     
  2. jcsd
  3. Oct 22, 2008 #2
    For the first one, what is the formula for e^x? That should make the proof obvious.

    For the second one, I don't know, and dinner's ready, but it probably follows from using the epsilon-delta definition of a limit.
     
  4. Oct 22, 2008 #3

    Dick

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    Hint: (a0+a1)*(b0+b1)=a0*b0 + (a0*b1+a1*b0) + a1*b1. In the first term the indices sum to 0, in the second to 1 and in the last to 2. Do you see how that is related to what you are asking?
     
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