Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle. It is named after Blaise Pascal in much of the western world, although other mathematicians studied it centuries before him in Ancient Greece, India, Persia, China, and Italy.
During the development of a general formula to calculate the final number of terms of any polynomial raised to any power it was determined that Pascal’s triangle had the answer. The way the terms of a polynomial interact with each other is a matter of combinatorial theory.
Positions for factorial and binomial coefficients in Pascal’s triangle
0
0 1
0 1 2
0 1 2 3
0 1 2 3 4 …
0
0 1
0 1 2
0 1 2 3
0 1 2 3 4 …
Leads to: (e k ).
Where :
e= Exponent and
k= Position
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