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Homework Help: Infinite series proof

  1. Oct 24, 2005 #1
    Hi,
    I'm working on this problem:
    If {s_n} is a nondecreasing sequence and s_n>=0, prove that there exists a series SUM a_k with a_k>=0 and s_n = a_1 + a_2 + a_3 + .......+ a_n.
    I'm not sure where to start. I wrote out the sequence's terms:
    s_n = (s_1, s_2, s_3, .....s_n)
    Then I wrote;
    s_1=a_1
    s_2=a_1+a_2
    .
    .
    s_n=a_1+a_2+......a_n
    I'm unclear about exactly what I need to go for.
    Any clarifiction will be greatly appreciated.
    CC
     
  2. jcsd
  3. Oct 24, 2005 #2

    shmoe

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    Science Advisor
    Homework Helper

    Try to write the a's in terms of the s's. You've already got a_1=s_1. What must a_2 be? a_3? a_4? a_n?
     
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