Blaise Pascal discovered the Pascal's Triangle.It's a Triangluar Array (Equilateral).
Many of us come to know about it. There are few secrets among it. I would like to share with all of you.
I hope you enjoy.
The Construction
The First and last values are always 1.
The middle values are obtained by adding two adjacent values in the upper row.
For eg: Six rows are shown here
It's not necessary that, there must be only 5 rows. We can construct many rows.
For Clear Understanding Purpose, I have changed the Equilateral Triangle to Right angled triangle.
Here's the triangle shown below:
The Second Column, marked in Red; shows values which increases with increment value of 1.
The Third Column, marked in Purple are triangular numbers.
Triangluar Numbers are number of dots which are used to represent a triangle. You can understand clearly with the photo below:
Consider a series of values in a column. Sum them up, you can see the answer in the adjacent column, but one row below.
The sum of the values in a row are denoted by 2^n
This photo shows how it's used in Binomial Coefficients
This photo shows how it's used in Probability Theory
Many of us come to know about it. There are few secrets among it. I would like to share with all of you.
I hope you enjoy.
The Construction
The First and last values are always 1.
The middle values are obtained by adding two adjacent values in the upper row.
For eg: Six rows are shown here
It's not necessary that, there must be only 5 rows. We can construct many rows.
For Clear Understanding Purpose, I have changed the Equilateral Triangle to Right angled triangle.
Here's the triangle shown below:
The Second Column, marked in Red; shows values which increases with increment value of 1.
The Third Column, marked in Purple are triangular numbers.
Triangluar Numbers are number of dots which are used to represent a triangle. You can understand clearly with the photo below:
Consider a series of values in a column. Sum them up, you can see the answer in the adjacent column, but one row below.
The sum of the values in a row are denoted by 2^n
This photo shows how it's used in Binomial Coefficients
This photo shows how it's used in Probability Theory
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