Putting Pascal’s Triangle into Formal Terms

Pascal’s triangle I notice is a large triangle containing many smaller triangles in its interior. The two outer edges of the triangle are made up of the number 1.  As we move down a level from the peak we create new triangles.  Now you must follow a vertical line from the peak of this outer triangle to the bottom of the triangle to understand my next explanation.  Each time we move down this vertical line from the peak we get a larger number. This number is determined by adding the sum of the previous interior triangles steps. For example, The first number after following our vertical line down the center of our original outer triangle is 2. We get this total by adding 1+1, which is the first two steps that bring us down to this level of our vertical line. The next number on this vertical line is 6. We get this sum by adding the previous 3 steps sum which is 1+2+3. So each time we take a step down this original vertical line we add another step in our sum.  Once you determine the pattern, you can repeat this process to expand outward in the triangle.


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