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Conditional identity

  1. Mar 13, 2014 #1
    1. The pratement, all variables and given/known data
    If a =1÷(1-b) ,b=1÷(1-c),c=1÷(1-d) prove that a=d


    2. Relevant equations



    3. The attempt at a solution
    a=1÷(1-b)
    a-1÷(1-b)=0
    {a(1-b)-1)}÷1-b=0
    a-ab-1=0
    a-ab=1
    similarly
    b-bc=1
    c-cd=1
    could any of you please give a hint, this was on test for 4 marks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 13, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    You are given
    [tex]
    b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}
    [/tex]
    Simplify the right hand side and then use
    [tex]
    a = \frac{1}{1 - b}.
    [/tex]
     
  4. Mar 13, 2014 #3
    pasmith thanks for your time I finally got it
    actually I hesitated to post such easy problems (for this PF level)
    good to see you taking time on helping me
    by the way how do you write fractions?
     
  5. Mar 13, 2014 #4

    adjacent

    User Avatar
    Gold Member

    Use Latex
    Click on the sigma sign on the Advanced editor for references.
    Use two #s around the code.
    For example \frac{1}{2} and putting two #s around will give ##\frac{1}{2}##
    If you want to see what others used,right click on the rendered Latex code,>Show Math as> Tex commands.
    Pasmith used this Code:
    b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}
     
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