Results 1 to 2 of 2

Math Help - Infinite series : testing for convergence, exponential involved.

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Infinite series : testing for convergence, exponential involved.

    I am asked to see if the summation of (3^n+n)/(4^n-3^n) converge or not.

    I have tried ratio test, comparison test and limit comparison test, but none of them work (at least for me provided my limited skills in math)

    By comparison test I used 3^n/4^n and 1/(4^n-3^n) for comparison, the same goes for limit comparison (I break the summation up into two part, one with 3^n on top and the other with n on top)

    How should I attack the problem? Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by kyva1929 View Post
    I am asked to see if the summation of (3^n+n)/(4^n-3^n) converge or not.

    I have tried ratio test, comparison test and limit comparison test, but none of them work (at least for me provided my limited skills in math)
    As these terms are all positive we do not need to take absolute values, but you can imagine they are present if you like:

    Divide through top and bottom by 3^n to get:

    \frac{3^n+n}{4^n-3^n}=\frac{1+n/3^n}{(4/3)^n-1}

    and for n sufficiently large the right most term is less than \frac{2}{(4/3)^n/2} so:

    \frac{3^n+n}{4^n-3^n}<\frac{4}{(4/3)^n}=4 (3/4)^n

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Another series I'm testing for convergence....
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 21st 2011, 10:19 PM
  2. Testing convergence of a series.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 2nd 2010, 07:52 PM
  3. Testing for Convergence of Series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 8th 2010, 03:48 PM
  4. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  5. Testing series for convergence
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 8th 2008, 08:45 PM

Search Tags


/mathhelpforum @mathhelpforum