Calculus 3 - Converge or Diverge?

Question

Alright. I've hit a small wall in my calculus series. I really don't know how to solve and prove if it converges or diverges.

an = ln(n+1) - ln(n)

I believe this converges to zero, but I'm not sure how to prove that it does and then I have no Idea how to find the sum of the sequence, if it does in fact converge. If you could help, that would be awesome. Thanks!

ted s · Accepted Answer

it certainly converges to 0...have you forgotten the properties of logs ??

and as for the sum...just write off the first 3 terms and it SHOULD give you an indication of the answer....{telescope}

Anonymous · Answer

that converges to zero

i know this because ln(n+1) - ln(n) = ln( (n+1)/n ) 
the right side converges to ln(1) = 0
done

another way to show this is to use the fact that ln ' (x) = 1/x, 

1/x approaches 0, then use the mean value theorem

to find the sum, just notice that there's a lot of cancelation

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Calculus 3 - Converge or Diverge?

2 Answers