A pattern

  • Thread starter JDude13
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  • #1
JDude13
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I have a pattern which I am having trouble working out the equation for...
It goes:

[tex]S=0, x_0=\frac{1}{1}[/tex]

[tex]S=1, x_0=\frac{0}{2}[/tex]

[tex]S=2, x_0=\frac{2}{4}[/tex]

[tex]S=3, x_0=\frac{0}{8}[/tex]

[tex]S=4, x_0=\frac{6}{16}[/tex]

[tex]S=5, x_0=\frac{0}{32}[/tex]

[tex]S=6, x_0=\frac{20}{64}[/tex]
[tex]\vdots[/tex]

I know it has something to do with
[tex]\frac{1+cos(\pi S)}{2}[/tex]

I have left the fractions unsimplified to show the relationship with the denominator and S as

[tex]DENOMINATOR=2^s[/tex]
 
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Answers and Replies

  • #2
36,344
8,297
Your formula breaks down at ##x_4## and ##x_6##. As your formula stands, ##x_S = \frac{1 + \cos(\pi S)}{2^S}##, the numerator will always be 0 or 2.
 

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