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Tricky calculus question - i've got problems

  1. Feb 28, 2010 #1
    Let (an) be a sequence of positive real numbers, decreasing and the sum of whose terms is infinite. Prove that the series whose general term is min(an, 1/n) is also divergent.

    I'm sorry but I'm no where with it. Could someone tell me if this is too difficult?

  2. jcsd
  3. Mar 1, 2010 #2
    I think that all you have to show here is that it is a monotonic decreasing sequence

    nth term -> min (an or 1/n)

    for nth+1 term -> min (an+1 or 1/(n+1))

    the 'min' function says that you choose 1/n or something lower than 1/n

    so you can tell for sure that

    an+1 < an
  4. Mar 1, 2010 #3
    I'm still stumped. Why don't you let me off and show the solution :D :D ;D
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