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Series/Sequence intuition

  1. Nov 3, 2013 #1
    Just wanted to know if I'm approaching this problem correctly.

    1. The Problem

    A. If the terms of a sequence of all positive terms go to zero, then the sequence must converge? True or false. Provide an example.

    B.If the terms of a series of all positive terms go to zero, then the series converges? True or false. Provide an example.

    2. Attempt

    A. True, consider the sequence ace sub n, starting at n = 0 and going to infinity, where ace sub n is 1/(n^4+2)

    The terms of this sequence decrease to zero and the sequence converges and the limit is 0.

    B. False, consider the Harmonic series 1/n, the limit as n--->inf = 0, but the terms do not decrease to 0.
     
  2. jcsd
  3. Nov 3, 2013 #2

    LCKurtz

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    Please restate B more completely and carefully and be sure you answer the question. It is asking about a series.
     
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