Properties of Pascal’s triangle –

Observing Pascal’s Triangle it is possible to notice some characteristics that are considered its properties. Among them, the following stand out:

  • First and last element of a line.

All lines of Pascal’s triangle will have their first and last elements equal to 1.

We say this because the 1st element of a line is represented by = 1 and the last is represented by = 1. Therefore, n must always be a natural number.

This property states that equidistant elements (binomial coefficients) belonging to the same line have equal numerical values. See examples.

Consider the 3rd line:

Consider the 5th line:

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Considering Pascal’s triangle represented by the numerical values 鈥嬧媜f its elements (binomial coefficients), we will realize that the sum of two elements in each row will be equal to the element below.

This property can be represented in equation form:

taking into account that n is greater than or equal to p.

  • Sum of the elements of a line.

The sum of the elements in a row with numerator n will be equal to 2n.

By Danielle de Miranda
Graduated in Mathematics