Results 1 to 2 of 2

Thread: [SOLVED] How do I find this value?

  1. #1
    Member
    Joined
    May 2009
    Posts
    99

    [SOLVED] How do I find this value?

    Find the value of $\displaystyle \frac{1}{2.3} + \frac{1}{3.4} + \frac {1}{4.5} + ... + \frac{1}{50.51} $

    THis is my take on the question:
    n = 49

    Using method of difference,

    f(r) = $\displaystyle -\frac{1}{r + 2}$
    f(r - 1) = $\displaystyle -\frac{1}{r+1} $
    Hence,
    f(n) - f(1 - 1) = $\displaystyle 1 - \frac{1}{n + 2}$

    When I sub n = 49 into this equation, I found $\displaystyle \frac{50}{51}$ which is not the same as the answer of $\displaystyle \frac{49}{102}$

    Where have I gone wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Thanks
    1
    Quote Originally Posted by mark1950 View Post
    Find the value of $\displaystyle \frac{1}{2.3} + \frac{1}{3.4} + \frac {1}{4.5} + ... + \frac{1}{50.51} $

    THis is my take on the question:
    n = 49

    Using method of difference,

    f(r) = $\displaystyle -\frac{1}{r + 2}$
    f(r - 1) = $\displaystyle -\frac{1}{r+1} $
    Hence,
    f(n) - f(1 - 1) = $\displaystyle 1 - \frac{1}{n + 2}$

    When I sub n = 49 into this equation, I found $\displaystyle \frac{50}{51}$ which is not the same as the answer of $\displaystyle \frac{49}{102}$

    Where have I gone wrong?
    Hi

    Firstly , we know the general term is $\displaystyle \frac{1}{(r+1)(r+2)}$

    Then do partial fraction here , we get

    $\displaystyle \sum^{49}_{r=1}[\frac{1}{r+1}-\frac{1}{r+2}]$

    Here let $\displaystyle f(r)=\frac{1}{r+1}$ , then $\displaystyle f(r+1)=\frac{1}{r+2}$

    so

    $\displaystyle \sum^{49}_{r=1}[f(r)-f(r+1)]$

    $\displaystyle = f(1)-f(50)$

    $\displaystyle =\frac{1}{1+1}-\frac{1}{50+1}$

    Continue from here , you should get the answer .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] p.d.f; how do I find the c.d.f?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Mar 15th 2010, 06:09 PM
  2. [SOLVED] find the value of B
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Jan 31st 2010, 11:53 PM
  3. [SOLVED] How do I find tan?
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: Feb 10th 2009, 04:00 PM
  4. [SOLVED] find the value of x
    Posted in the Geometry Forum
    Replies: 4
    Last Post: Mar 28th 2008, 09:06 PM
  5. [SOLVED] what does it mean to find the mean
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 15th 2007, 02:18 PM

Search Tags


/mathhelpforum @mathhelpforum