Results 1 to 10 of 10

Math Help - Induction help needed please

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    50

    Induction help needed please

    Define the sequence (L_n) by
    L_n=1/(n+1)+1/(n+2)+1/(n+3)+ … + 1/2n for n ≥1

    Show using an inductive or non-inductive argument that

    L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1

    and

    L_n<n(1/(n +1)) for n ≥2

    Many thanks.
    Last edited by alpha; January 19th 2010 at 03:51 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by alpha View Post
    Show using an inductive or non-inductive argument that

    L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1

    Many thanks.
    You do realize you did not even say what L_n is, right?! The logical assumption is that they are the Lucas numbers. But, this doesn't seem to be true then.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    50
    Sorry for the mistake. I just corrected the question.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by alpha View Post
    Define the sequence (L_n) by
    L_n=1/(n+1)+1/(n+2)+1/(n+3)+ + 1/2n for n ≥1

    Show using an inductive or non-inductive argument that

    L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1

    and

    L_n<n(1/(n +1)) for n ≥2

    Many thanks.
    Hint: L_n=H_{2n}-H_n where H_n is the n-th harmonic number. That should make things easier.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2009
    Posts
    50
    not clear about this. would help if you showed me what the answer would like. thanks.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by alpha View Post
    not clear about this. would help if you showed me what the answer would like. thanks.
    It would help you more if you did at least some of it and reported back with any problems.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Nov 2009
    Posts
    50
    Sorry but the whole problem is that I cant do this question at all.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by alpha View Post
    Sorry but the whole problem is that I cant do this question at all.
    What's induction?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Nov 2009
    Posts
    50
    i dont know
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by alpha View Post
    i dont know
    Are you serious? Why would you be given a problem you aren't equipped to solve.

    Mathematical induction - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Help needed for induction proof
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: June 5th 2011, 07:53 AM
  2. Proof of summation of i^3 by induction, help needed
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 20th 2009, 12:24 AM
  3. Induction help needed
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: February 4th 2009, 04:49 AM
  4. Replies: 2
    Last Post: December 4th 2008, 01:51 AM
  5. A proof with induction, really needed!
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 5th 2008, 10:34 AM

Search Tags


/mathhelpforum @mathhelpforum