thanks,,,, my course (which was very word intensive) Never used the term "expand", but went into depth on simple problems with pascals triangle. I think now I understand the principle behind the problems.
You are welcome - good luck !
That's great to hear! Pascal's triangle is a fascinating mathematical concept that has various applications in algebra, combinatorics, and number theory. It's often used to solve problems related to binomial coefficients and for understanding the patterns in the triangle itself.
If you want to explore more about Pascal's triangle and understand its principles further, here's a step-by-step guide on how to get started:
1. Learn the basic construction: Pascal's triangle is constructed by starting with a row containing only the number 1. Each subsequent row is formed by adding the numbers directly above and diagonally above to get the number below. For example, the third row would be [1, 1], and the fourth row would be [1, 2, 1].
2. Explore patterns: Look for patterns within the triangle. One of the most famous patterns is that the numbers on the edges of the triangle are always 1. Additionally, each number in the triangle is the sum of the two numbers directly above it. Investigating these patterns can help you understand the principles behind Pascal's triangle.
3. Understand binomial coefficients: Pascal's triangle is closely related to binomial coefficients, often denoted as C(n, k). These coefficients represent the number of ways to choose k elements from a set of n elements. For example, C(4, 2) is equal to 6 because there are six ways to choose 2 elements from a set of 4 elements. Pascal's triangle provides a convenient way to find these coefficients without calculating each one individually.
4. Practice solving problems: Look for problem-solving exercises or examples that involve Pascal's triangle. These could include finding specific numbers or coefficients within the triangle, determining the sum of a row or diagonal, or using Pascal's triangle to solve other mathematical problems.
5. Utilize online resources: There are numerous online resources, videos, and tutorials available that delve into Pascal's triangle in detail. These resources can provide additional examples, explanations, and practice problems to enhance your understanding.
Remember, learning any mathematical concept requires consistent practice and exploration. By applying these steps and engaging in continuous learning, you'll be able to further expand your knowledge of Pascal's triangle and its principles.