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Summing a sequence

  1. Jan 1, 2012 #1
    I've created two summations for my coursework, now I need to show whether or not the summations are finite or infinite.

    The 2 summations are very similar:


    With the n/2 removed it was easy enough to show the sum was equal to 1 [edit: I now realise I may have this wrong], now with the n/2 term added I really have no idea where to start.

    Any help appreciated, thanks.

    Edit: I can see my writing may not be legible, 1's in the pic are straight vertical lines, some of the 2's may look like 1's, but they are 2's.
    Last edited: Jan 1, 2012
  2. jcsd
  3. Jan 1, 2012 #2


    Staff: Mentor

    For the first one, I found that the terms in the sequence approach a positive number. This is enough to convince me that the first series diverges.
  4. Jan 1, 2012 #3
    Thanks for the reply!

    Does this mean it sums to infinity?

    What were your steps to find that it approaches a positive number?
  5. Jan 2, 2012 #4


    Staff: Mentor

    Your textbook should have definitions for the terms converges and diverges.
    I took the limit of the nth term in the sequence.
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