1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proving the convergence of a sequence

  1. Mar 9, 2009 #1
    [tex]2 ,2+\frac{1}{2},2+\frac{1}{2+\frac{1}{2}}[/tex]
    etc..
    (the sequence consists only from positive number so the sum is not negative)
    in order to prove that its convergent i need to prove monotonicity and boundedness

    monotonicity:(by induction)

    [tex]a_1=2[/tex]
    [tex]a_2=2.5[/tex]
    so i guess its increasing
    suppose n=k is true:
    [tex]a_{k-1}<a_k[/tex]
    prove n=k+1 ([tex]a_{k}<a_{k+1}[/tex])
    [tex]
    a_k>a_{k-1}\\
    [/tex]
    [tex]
    \frac{1}{a_k}<\frac{1}{a_{k-1}}\\
    [/tex]
    [tex]
    2+\frac{1}{a_k}<2+\frac{1}{a_{k-1}}\\
    [/tex]
    [tex]
    a_{k+1}<a_k
    [/tex]

    i proved the opposite :)
    so this is weird.

    the answer in the book tells me to split the sequence into odd /even sub sequences
    the one is ascending and the other its descending.

    i cant see how many sub sequences i need to split it to
    maybe its 5 or 10
    what is the general way of solving it.
    and how you explained that i proved the opposite
     
    Last edited: Mar 9, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: Proving the convergence of a sequence
Loading...