Difference between revisions of "Power's of 2 in pascal's triangle"

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== Pascal's Triangle ==
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= Review =
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== Pascal's Triangle ==  
  
 
Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers above it. It Looks something like this:
 
Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers above it. It Looks something like this:
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   1 4 6 4 1
 
   1 4 6 4 1
 
And on and on...
 
And on and on...
1+1=2
 
1+2=3
 
1+3=4
 
  
 
== Patterns and properties ==
 
== Patterns and properties ==
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                 <math>\binom{1}{0}</math>                  <math>\binom{1}{1}</math>
 
                 <math>\binom{1}{0}</math>                  <math>\binom{1}{1}</math>
 
     <math>\binom{2}{0}</math>                    <math>\binom{2}{1}</math>                <math>\binom{2}{1}</math>
 
     <math>\binom{2}{0}</math>                    <math>\binom{2}{1}</math>                <math>\binom{2}{1}</math>
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And on and on...
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Remember that <math>\binom{n}{r}=\frac{n!}{k!(n-k)!}</math> where <math>n\ger</math>.

Revision as of 13:54, 16 June 2019

Review

Pascal's Triangle

Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers above it. It Looks something like this:

      1
     1 1
    1 2 1
   1 3 3 1
  1 4 6 4 1

And on and on...

Patterns and properties

Pascal's Triangle can also be written like this

                           $\binom{0}{0}$
                $\binom{1}{0}$                  $\binom{1}{1}$
   $\binom{2}{0}$                     $\binom{2}{1}$                $\binom{2}{1}$

And on and on... Remember that $\binom{n}{r}=\frac{n!}{k!(n-k)!}$ where $n\ger$ (Error compiling LaTeX. Unknown error_msg).