Results 1 to 9 of 9

Math Help - sequence 2

  1. #1
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    sequence 2

    General term in a sequence is an=4n+8/(n+5)
    What is the sum of greatest lower bound of the sequence and lowest upper bound f the sequence. I got the answer as 5 but it must be 6.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: sequence 2

    Quote Originally Posted by kastamonu View Post
    General term in a sequence is an=4n+8/(n+5)
    What is the sum of greatest lower bound of the sequence and lowest upper bound f the sequence. I got the answer as 5 but it must be 6.

    If n\in\mathbb{Z}^+ then 2\le\frac{4n+8}{n+5}\le 4.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    Re: sequence 2

    How did you find it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    440
    Thanks
    86

    Re: sequence 2

    VERY EASY...FIND the first term a1=...2 and then the lim of the sequence =4.....then think...it is easy.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    Re: sequence 2

    I tried to find the answer by evaluating the fraction. Yes that way is better. Limit is 4.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    Re: sequence 2

    4n+8 4n+20-20+8
    ---- = ----------
    n+5 n+5

    12
    = 4 - ---
    n+5 .

    Sequence is increasing and lower bound is 2(If we take n=1). If we
    find the limit according to infinity upper bound is 4. But I wanted to
    find it by using inequality method.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,531
    Thanks
    1389

    Re: sequence 2

    \frac{4n+8}{n+5}\le A is, since n+ 5 is positive, the same as 4n+ 8\le A(n+ 5)= An+ 5A. (A- 4)n\ge 8- 5A. If we want this to be true for all n, we must have A= 4.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    Re: sequence 2

    many thanks
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,487
    Thanks
    1391

    Re: sequence 2

    Quote Originally Posted by kastamonu View Post
    General term in a sequence is an=4n+8/(n+5)
    What is the sum of greatest lower bound of the sequence and lowest upper bound f the sequence. I got the answer as 5 but it must be 6.
    \displaystyle \begin{align*} \lim_{n \to \infty} \frac{4n + 8}{n + 5} &= \lim_{n \to \infty} \frac{4n + 20 - 12}{n + 5} \\ &= \lim_{n \to \infty} \left[ \frac{4(n + 5)}{n + 5} - \frac{12}{n + 5} \right] \\ &= \lim_{n \to \infty} \left( 4 - \frac{12}{n + 5} \right) \\ &= 4 - 0 \\ &= 4 \end{align*}

    So the least upper bound is 4.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 24th 2010, 02:10 AM
  2. Replies: 0
    Last Post: July 4th 2010, 12:05 PM
  3. Replies: 2
    Last Post: March 1st 2010, 11:57 AM
  4. sequence membership and sequence builder operators
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: June 4th 2009, 03:16 AM
  5. Replies: 12
    Last Post: November 15th 2006, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum