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How to prove by mathematical induction?

  1. Feb 3, 2013 #1
    How do I prove a formula/rule or something by mathematical induction? Please give me a few examples or resources and explain it as best you can because I think I'm messing up some how.
     
  2. jcsd
  3. Feb 3, 2013 #2
    What are you not getting, exactly? If you just don't know what induction is, surely a google search would be faster than starting a new thread.
     
  4. Feb 3, 2013 #3
    Everything I read confuses me, it tells me to do something different everytime...
     
  5. Feb 3, 2013 #4
    We can't help you if you don't explain what's confusing you. Try posting your attempt at solving an induction problem and explain where you get stuck.
     
  6. Feb 3, 2013 #5
    I have an equation, (5n + 2) = 2[(5/2)n + 1] I know this is true from the basis step. Then I asume n = k now I must prove n = k + 1. So, (5k + 2) = 2[(5/2)k + 1]

    Alright then, I try to substitute k + 1 in and add it or something so I get... 2[(5/2)k + 1] + [5(k + 1) + 2] = 2 [(5/2)(k + 1) + 1]

    Simplifying, I get 10k + 2 + 5k + 5 + 2 = 10(k + 1) + 2

    And finallly, 15k + 9 =/= 10k + 12

    SO.... whaaaat? What happened here?
     
  7. Feb 4, 2013 #6
    (5n + 2) = 2[(5/2)n + 1]

    n = 0:
    5*0 + 2 = 2[(5/2)*0 + 1]

    The case is true for 0.

    Suppose the case is true for n = k.
    Now we can use (5k + 2) = 2[(5/2)k + 1].

    n = k + 1:
    5(k + 1) + 2 = (5k + 2) + 5 = 2[(5/2)k + 1] + 5 = 2[(5/2)k + 1 + 5/2] = 2[(5/2)(k+1) + 1]

    The case n = k + 1 follows from the case n = k.
    With case n = 0 true the equation therefore works for all non-negative integers.
     
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