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A proof question

  1. Nov 27, 2008 #1
    i am given a real and positive number a1 a2 a3 ...
    which goes by a(n)<=c*a(n-1) for every n=>2 for a certain given number c>0 .

    prove that
    a(n)<=a(1)*c^(n-1)

    ??

    a(n) is the n'th number of the series
     
  2. jcsd
  3. Nov 27, 2008 #2

    nicksauce

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    Use a proof by induction. It should be fairly straight forward.
     
  4. Nov 27, 2008 #3
    i dont have a base case here

    and there are two variables

    ??
     
  5. Nov 27, 2008 #4
    Use induction of n. Your base case would be n=2.
     
  6. Nov 27, 2008 #5
    for n=2
    i get
    a(2)=c*a(1)

    this base case doesnt prove anything

    ??
     
  7. Nov 27, 2008 #6

    nicksauce

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    The base case is trivially true, since it is the same condition for the members of the sequence.
     
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