(1.0 / 2) process repeated 5 times; what is the algrabraic formula?

  1. 1 / 2 = 0.5
    0.5 / 2 = 0.25
    0.25 / 2 = 0.125
    0.125 / 2 = 0.0625
    0.0625 / 2 = 0.03125

    What is the algebraic formula for this?
     
  2. jcsd
  3. jgens

    jgens 1,621
    Gold Member

    [itex]\frac{1}{2^5}[/itex]
     
  4. This is a new one;

    64 / 2 = 32
    32 / 2 = 16
    16 / 2 = 8
    8 / 2 = 4
    4 / 2 = 2
    2 / 2 = 1
    1 / 2 = 0.5
    0.5 / 2 = 0.25
    0.25 / 2 = 0.125
    0.125 / 2 = 0.0625
    0.0625 / 2 = 0.03125

    [itex]\frac{64}{2^{10}}[/itex]
     
    Last edited: Mar 31, 2012
  5. Thanks.
     
  6. jgens

    jgens 1,621
    Gold Member

    That should actually be [itex]\frac{64}{2^{11}}[/itex].

    Edit: Enclose your "10" in { } to make it appear correctly.
     
  7. Your right, I added one too many and thought there was only ten.
     
  8. Thanks for the editing tip.
     
  9. Char. Limit

    Char. Limit 1,986
    Gold Member

    But that's not a formula.

    [tex]\frac{1}{2^n}[/tex] is a formula.
     
  10. jgens

    jgens 1,621
    Gold Member

    I could nitpick and argue that [itex]\frac{1}{2^n}[/itex] is actually an expression and not a formula since it does not contain an equals sign; but the distinction is really not all that relevant. The OP wanted to know how to express "1 divided by 2 fives times" algebraically and one way is [itex]\frac{1}{2^5}[/itex]. I really don't understand the objection.
     
  11. Mentallic

    Mentallic 3,699
    Homework Helper

    Also notice that since we divided 64 by 2 five times and we got to 1, so [itex]\frac{64}{2^5}=1[/itex] rearranging, we get [itex]64=2^5[/itex] so we can express the answer as

    [tex]\frac{64}{2^{10}}=\frac{2^5}{2^{10}}[/tex]

    And if you remember the rule of indices, [tex]\frac{2^a}{2^b}=2^{a-b}[/tex] so [tex]\frac{2^5}{2^{10}}=2^{5-10}=2^{-5}=\frac{1}{2^5}[/tex]

    As we got in your first question.
     
  12. rcgldr

    rcgldr 7,514
    Homework Helper

    The formula (not sure if this is considered algebraic) or notation for a product series in the original example would be:

    [tex]\prod_{i=1}^5 \ \frac{1}{2} [/tex]
     
    Last edited: Apr 2, 2012
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