How do I find binomial coefficients for long numbers using Pascal Triangle?

In summary, the Pascal Triangle Problem is a mathematical problem that involves creating a triangular pattern of numbers, known as the Pascal Triangle. To construct it, start with a 1 at the top and follow a specific pattern of adding numbers from the row above. This triangle has many applications in mathematics and can be extended to include other elements. It also has interesting properties and connections to other areas of math.
  • #1
TonyC
86
0
Trying to find the binomial coeffiecients of
9....9
and
6....9

How do I do this?
 
Physics news on Phys.org
  • #2
I'm not sure what you mean by 9...9 etc. but you can calculate the binomial coefficient simply as n!/(r!(n-r)!)
 
  • #3


The Pascal Triangle is a mathematical tool used to find the coefficients of binomial expansions, such as (a+b)^n. To find the coefficients for (9....9) and (6....9), you can use the formula (n choose k), where n is the number of terms in the expansion (in this case, the number of 9s) and k is the term number you are trying to find the coefficient for. For (9....9), n=9 and k=9, so the coefficient is 1. For (6....9), n=10 and k=9, so the coefficient is 10. If you are unfamiliar with the Pascal Triangle, there are many online resources and tutorials available to help you understand and use it effectively.
 

FAQ: How do I find binomial coefficients for long numbers using Pascal Triangle?

1. What is the Pascal Triangle Problem?

The Pascal Triangle Problem is a mathematical problem that involves creating a triangular pattern of numbers, known as the Pascal Triangle. Each number in the triangle is the sum of the two numbers above it, forming a symmetrical shape.

2. How do you construct a Pascal Triangle?

To construct a Pascal Triangle, start with a 1 at the top of the triangle. Then, for each subsequent row, add a 0 to the beginning and end of the previous row, and add the two adjacent numbers to get the numbers in between. Repeat this process until the desired number of rows is achieved.

3. What is the significance of the Pascal Triangle?

The Pascal Triangle has many applications in mathematics, including calculating binomial coefficients, finding patterns in number sequences, and solving certain types of probability problems.

4. Can the Pascal Triangle be extended to more than just numbers?

Yes, the Pascal Triangle can be extended to include other types of elements, such as letters or geometric shapes. This can be useful in visualizing patterns and solving more complex problems.

5. Are there any other interesting properties of the Pascal Triangle?

Yes, the Pascal Triangle has many interesting properties, such as the fact that the sum of the numbers in each row is equal to the power of 2, and that the numbers in the triangle follow the Fibonacci sequence. It also has connections to many other areas of mathematics, such as fractals and graph theory.

Back
Top