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

There are at least 2 ways of prooving it.

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:

2) You can construct in graphically:

First row consists of a single number

Second row consists of 2 numbers

In all other rows first and last numbers are

The picture shows 10 rows of the triangle.

By signing up, you agree to our Terms of Service and Privacy Policy

The sixth row in Pascal's Triangle represents the coefficients of the sixth-degree polynomial when expanded from ( (a + b)^5 ). Each number in the row corresponds to a term in the expansion, and the values are obtained using combinations (binomial coefficients). Specifically, the numbers in the row correspond to the binomial coefficients of the form ( \binom{5}{k} ), where ( k ) ranges from 0 to 5. These coefficients are symmetric because of the symmetry property of Pascal's Triangle, hence why the row appears as 1, 6, 15, 20, 15, 6, 1.

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7