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Proof by induction

  1. Mar 1, 2009 #1
    I need help to solve this problem

    Use induction to prove that, for n>=0:

    3*5^0 + 3*5^1 + 3*5^2 + 3*5^3 + ...+ 3*5^n = 3*(5^(n+1)-1)/4

    in other word


    n

    [tex]\sum[/tex] 3*5 k= 3*(5 n+1-1) / 4
    k= 0
     
  2. jcsd
  3. Mar 1, 2009 #2

    rock.freak667

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    Homework Helper

    Assume true for n=N and now prove true for n=N+1.
    Do you know how to do a proof by induction?
     
  4. Mar 1, 2009 #3
    I did these steps and I tried to complete the rest but I don't know some of the steps

    and what I is in the attached doc.
     

    Attached Files:

  5. Mar 1, 2009 #4

    rock.freak667

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    Homework Helper

    Try not to upload word documents as these usually contain viruses. Can you type out the steps you did?
     
  6. Mar 1, 2009 #5
    Basis: n= 0
    0
    [tex]\sum [/tex]3*5^ 0 = 3

    k= 0




    3*(5 0+1-1) / 4 = 3




    Assume:

    n

    [tex]\sum[/tex] 3*5^k= 3*(5 n+1-1) / 4
    k= 0



    Prove:

    n+1

    [tex]\sum[/tex] 3*5 ^k= 3*(5 (n+1)-1) / 4
    k= 0


    ________________________________________
    Proof:

    n+1
    [tex]\sum[/tex] 3*5^ k =

    k= 0
     
  7. Mar 1, 2009 #6
    As you have the base case, think about the sum:

    3*5^0 + 3*5^1 + 3*5^2 + 3*5^3 + ...+ 3*5^n + 3*5^(n+1)

    which is now your inductive step, as rock.freak667 suggested.

    What are the two ways in which this can also be written with the information you already have?

    The Bob
     
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