Results 1 to 2 of 2

Math Help - Proving converging and diverging

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    92

    Proving converging and diverging

    Show that if an > 0 and Σan is convergent, then Σln(1+an ) is convergent.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    limit comparison test with a_n, then let's compute \lim_{n\to\infty}\frac{\ln\big(1+a_n\big)}{a_n}, substitute t=a_n then t\to0 since a_n\to0 because of the convergence of the first series, thus \lim_{t\to0}\frac{\ln(1+t)}t=1 and the second series converges.

    or for each n\ge1 we have \ln(1+n)\le n then \ln(1+a_n)\le a_n and the rest follows by direct comparison test. (Comparison test does apply since a_n>0, so our work is okay.)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. converging or diverging?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: December 16th 2009, 09:13 PM
  2. diverging or converging?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 29th 2009, 07:26 AM
  3. diverging or converging?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 29th 2009, 07:15 AM
  4. Converging or Diverging...??
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 28th 2009, 10:07 PM
  5. converging or diverging?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 20th 2009, 06:26 PM

Search Tags


/mathhelpforum @mathhelpforum