If you're unsure of what Pascal's Triangle is...
Wikipedia wrote:In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy.[1]
The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number directly above and to the left with the number directly above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.
This construction is related to the binomial coefficients by Pascal's rule, which states that if
(x+y)^n=\sum_{k=0}^n{n \choose k}x^{n-k}y^{k}
then
{n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}
for any nonnegative integer n and any integer k between 0 and n.
Plotted out, it would look something like this.
There are but two rules; please post the row first, and any comments you may have under that, and NO CALCULATORS!
I shall start the chain with...
1
