Results 1 to 4 of 4

Math Help - Telescoping Series

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    2

    Telescoping Series

    Please write out how you did this as well. I'd like to understand and not just know the answer. Thanks

    <br />
\sum\limits_{n = 1}^\infty {ln (1+ (1/n))}<br />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562
    Quote Originally Posted by geniusboy91 View Post
    Please write out how you did this as well. I'd like to understand and not just know the answer. Thanks

    Σ from n=1 to ∞ of ln(1+(1/n))
    Just make a common denominator

    \sum_{n \geq 1} \left[ ln(1+\frac{1}{n})=ln(\frac{n+1}{n})=ln(n+1)-ln(n) \right]

    I think you can take it from here.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    2
    Ahh!!! I knew it would be some simple algebraic thing I was missing. And so that would lead to the sequence of patial sums being

    ln(n+1) - ln(1) = ln(n+1)

    and diverges because:

    <br />
\lim_{n\to\infty} {ln(n+1)}<br />
is infinity?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562
    Quote Originally Posted by geniusboy91 View Post
    Ahh!!! I knew it would be some simple algebraic thing I was missing. And so that would lead to the sequence of patial sums being

    ln(n+1) - ln(1) = ln(n+1)

    and diverges because:

    <br />
\lim_{n\to\infty} {ln(n+1)}<br />
is infinity?
    Correct.
    Since the sequence of the partial sums diverges then ,by the definition, the series diverges.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 13th 2011, 12:39 PM
  2. Telescoping series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 16th 2010, 07:18 AM
  3. Telescoping series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 25th 2009, 01:20 AM
  4. Telescoping Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 1st 2008, 06:00 PM
  5. Telescoping series sum
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 16th 2008, 07:20 PM

Search Tags


/mathhelpforum @mathhelpforum