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Calculus - Series

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Why is the limit of the sum n=1 to infinity of ln(2(n+1))–ln(2n) divergent? I thought it would be -ln2 because all the other terms cancel out cancel out.

  • Calculus - Series - ,

    L'Hopitals rule:

    (1/2n+2)(2n/1)

    2n/(2n+2)

    second application of the rule:
    2/2=1


    so at infinity, you are adding 1 + 1+ ...

    which means it is divergent.

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