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Recursion formula

  1. May 2, 2005 #1
    Can you write the recursion formula for this series?'
    a (then little n) = 1/2^n

    *the 2 is to the nth power, not the one
    *for the first half, it is written a then a little n to the bottom right.

    I don't understand how to even go about this. Any help would be great thanks.
  2. jcsd
  3. May 2, 2005 #2
    [tex]a_n =\frac{1}{2^n}[/tex]

    Write down some of the terms like [itex]a_0 =\frac{1}{2^0}, a_1=\frac{1}{2^1}, a_2=...[/itex] using this formula. Now a recursion relation is a relation that relates a term ([itex]a_n[/itex]) in this series to the previous term ([itex]a_{n-1}[/itex]). You are asked to find this relation. If you see the pattern in the terms it shouldn't be too difficult to write down [itex]a_n[/itex] in terms of [itex]a_{n-1}[/itex].
  4. May 2, 2005 #3


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    Staff Emeritus
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    First write out a few of those numbers and look at them!
    [tex]1, \frac{1}{2},\frac{1}{4},\frac{1}{8}...[/tex]

    Now think "how do you go from one number to the next?" (that's what recursion IS!). Looks to me like you multiply by 1/2!

    That is: a0= 1, an+1= (1/2)an.
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