Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook