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Infinite sums of logs.

  1. Jun 8, 2013 #1
    So I was trying to see if [itex]\Sigma[/itex]ln([itex]\frac{n}{n+1}[/itex]) diverges or converges. To see this I started writing out [ln(1) - ln(2)] + [ln(2) - ln(3)] + [ln(4) - ln(5)] ...

    I noticed that after ln(1) everything must cancel out so I reasoned that the series must converge on ln(1) which equals ZERO. However, Wolfram Alpha says the series is divergent. I tried looking it up how to do this problem and I read that the last term also does not cancel out which is why the series diverges. However, shouldn't there always be a term bigger than the last so everything must cancel.
     
  2. jcsd
  3. Jun 8, 2013 #2
    Write an expression for [itex] \sum_{k=1}^{n} ln(\frac{k}{k+1}) [/itex]. What is the limit of this expression as n tends to infinity?
     
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