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Mathematical induction and arithmetic progression

  1. May 7, 2010 #1
    1. The problem statement, all variables and given/known data
    All the terms of the arithmetic progression u1,u2,u3...,un are positive. Use mathematical induction to prove that, for n>= 2, n is an element of all positive integers,

    [ 1/ (u1u2) ] + [ 1/ (u2u3) ] + [ 1/ (u3u4) ] + ... + [ 1/ (un-1un) ] = ( n - 1 ) / ( u1un)


    2. Relevant equations



    3. The attempt at a solution
    I proved that P(2) is true. However, I tried to prove that P(K+1) is true but to no avail.

    Thanks.
     
  2. jcsd
  3. May 7, 2010 #2

    vela

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    Staff Emeritus
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    Use the fact that {un} is an arithmetic sequence along with

    [tex]\frac{1}{u_m} - \frac{1}{u_n} = \frac{u_n-u_m}{u_mu_n}[/tex]
     
  4. May 9, 2010 #3
    Solved. Thanks a lot!
     
  5. May 10, 2010 #4
    This helped a lot for me on the induction concept:

    http ://en. wikipedia. org/wiki/Mathematical_induction
     
  6. Jun 26, 2011 #5
    i know this thread is old... but i need a little help on the exact same question...

    i'm stuck at:

    [tex]P(k+1)=\frac{kU_{k+1}-U_{k+1}+U_1}{U_1U_kU_{k+1}}[/tex]

    i need to prove that this equals to:

    [tex]\frac{k}{U_1U_{k+1}}[/tex]

    but i can't see the link at all... is there something missing ?~
     
  7. Jun 27, 2011 #6

    Mark44

    Staff: Mentor

    What do you have for your induction hypothesis? I.e., P(k).
     
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