Why does the sixth row go 1, 6, 15, 20, 15, 6, 1?

1 Answer
Daniel L.
Sep 5, 2015

There are at least 2 ways of prooving it.

Explanation:

As I wrote you can calculate the elements of Pascal's Triangle in at least 2 ways:

1) Directly from the definition.

Each row consists of numbers: #(""_0^n)#, #(""_1^n)#,..., #(""_n^n)#, where:

#(""_k^n)=(n!)/(k!*(n-k)!#

2) You can construct in graphically:

First row consists of a single number #1#.
Second row consists of 2 numbers #1#
In all other rows first and last numbers are #1#, others are the sum of the 2 numbers in the row above.
The picture shows 10 rows of the triangle.

http://www.matematyka.pl/39688.htm

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