Pascal

Definition

Pascal's Triangle is a triangular array of the binomial coefficients. It has applications in algebra, combinatorics, and trigonometry.

5 Must Know Facts For Your Next Test

1. Each row in Pascal's Triangle corresponds to the coefficients of the expanded form of $(x + y)^n$ for $n = 0, 1, 2, \ldots$.
2. The elements in each row are symmetrical; they read the same forwards and backwards.
3. The sum of the elements in the $n$-th row is $2^n$.
4. Pascal's Triangle can be used to find combinations, represented as $\binom{n}{k}$ (read as 'n choose k').
5. In polar coordinates, Pascal’s Triangle assists in converting complex numbers into trigonometric forms by breaking down coefficients.

Review Questions

• How can you use Pascal’s Triangle to expand $(x + y)^4$?
• What is the value of $\binom{5}{2}$ using Pascal’s Triangle?
• Explain how symmetry in Pascal’s Triangle helps simplify calculations.

Related terms

Binomial Theorem: A formula that provides a quick way to expand a binomial raised to any positive integer power.

$\binom{n}{k}$: A binomial coefficient representing the number of ways to choose k elements from a set of n elements without regard to order.

$2^n$: Represents the sum of all elements in the n-th row of Pascal's Triangle.