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Pascal's triangle is a triangle that works in the following way.

The sum of the numbers in each row is 2 to the nth power. (Remember, the first row is row zero.)

## Properties

Except for the first column, if one alternates the sum and difference (difference first), the value is always 0.

For example,

Row 2: 1 - 1 = 0

Row 3: 1 - 2 + 1 = 0

Row 4: 1 - 3 + 3 -1 = 0

## Combinatorics approach

The triangle can also be viewed as follows:

This can be used to prove the identity that

$\sum_{k=0}^n\binom{n}{k}=2^n$

The $n$-th row of the triangle, starting with zeroth row, represents the coefficients of the binomial expansion $(a+b)^n$ .

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