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Prove a^(m+n) = a^m + a^n with mathematical induction

  1. Jan 16, 2012 #1
    prove by induction that, 1) a^(m+n) = a^m + a^n

    2) (a^m)^n=a^(mn)


    2. Relevant equations -- mathematical induction



    3. The attempt at a solution
    the equations hold for a = 1.
    let's say the equation hold for a = s; then s^(m+n) = s^m + s^n
    now for a = s+1; (s+1)^(m+n) = (binomial expansion of s+1)

    how can i prove that (s+1)^(m+n) = (s+1)^m * (s+1)^n
     
  2. jcsd
  3. Jan 16, 2012 #2

    D H

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    You can't prove that because it's not true. 22+1=23=8, 22+21=4+2=6, and 8 is obviously not equal to 6.

    What you can prove is that am^n = am*an.


    Wrong approach. Try starting with n=0 as your base case rather than a=1. And of course you do want to prove the corrected thesis.
     
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