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Problem on induction

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data

    Sn=1-3+5-7...+(-1)^n(2n+1)


    2. Relevant equations

    Show that Sn=(-1)^n(n+1)

    3. The attempt at a solution

    S(n+1)=Sn+(-1)^(n+1)*(2n+3) = (-1)^n*(n+1)+ (-1)^(n+1)*(2n+3)
    S(n+1)= (-1)^(n+1)*[(2n+3)-(n+1)] (because (-1)^(n+1)= - (-1)^n )
    S(n+1)=(-1)^(n+1)*(n+2)

    is that correct proof
     
    Last edited: Oct 15, 2011
  2. jcsd
  3. Oct 15, 2011 #2

    HallsofIvy

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    Well, you haven't shown that it is true for n= 1, so, no. But that is easily fixed.
     
  4. Oct 15, 2011 #3
    i did that before doing the work and for n=1 it came out to equal -3 and i also had to count S2 and S3 and i got 5 for S2 and -7 for S3.

    But my proof is fine right?
     
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