Revision as of 14:02, 16 June 2019

Review

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:

And on and on...

Pascal's Triangle can also be written like this

And on and on... Remember that $\binom{n}{r}=\frac{n!}{k!(n-k)!}$ where $n \ge r$ .

                1     =1
               1+1    =2
              1+2+1   =4
             1+3+3+1  =8
            1+4+6+4+1 =16

These are powers of two. Let's prove it true. (Note: There are dozens of more patterns but it would have nothing to do with powers of two).

@@ Line 13: / Line 13: @@
 == Patterns and properties ==
+=== Conbanations ===
 Pascal's Triangle can also be written like this
@@ Line 22: / Line 24: @@
 And on and on...
 Remember that <math>\binom{n}{r}=\frac{n!}{k!(n-k)!}</math> where <math>n \ge r</math>.
+=== Sum of rows ===
+     =1
++1    =2
++2+1   =4
++3+3+1  =8
++4+6+4+1 =16
+These are powers of two. Let's prove it true. (Note: There are dozens of more patterns but it would have nothing to do with powers of two).
+= Powers of two =