Look at the row immediately preceding, that is row 5. Do you notice anything special relating the numbers in row 5 to the numbers in row 6? The first and last number in each row is, of course, 1.gnome222 said:I am trying to find the equation to predict the next middle number in pascal's triangle. By middle number I mean in each row that has odd number of numbers the middle number of that row. So for example row 6 which has 1,6,15,20( middle number), 15,6,1. I am trying to find that middle number, but without any luck. Any suggestions?
numbers 2, 6, 20, 70, 252robphy said:Can you give explicit examples of "middle number" ?
http://www.wolframalpha.com/input/?i=pascal+triangle [click on the "More rows" button]
And then: 924, 3432, 1287, 48620, 184756, 705432gnome222 said:numbers 2, 6, 20, 70, 252
Svein said:You know that the number in Pascal's triangle, row n, place k (k=0 to n), is given by [itex]\frac{n!}{k!(n-k)!} [/itex]?
Svein said:And then: 924, 3432, 1287, 48620, 184756, 705432gnome222 said:numbers 2, 6, 20, 70, 252
The pattern in Pascal's triangle is a triangular array of numbers where each number is the sum of the two numbers above it. The first and last numbers in each row are always 1, and the remaining numbers are found by adding the two numbers above them.
Pascal's triangle is closely related to binomial coefficients, as the numbers in each row represent the coefficients in the expansion of (a + b)^n, where n is the row number. For example, the third row of Pascal's triangle (1 3 3 1) represents the coefficients in the expansion of (a + b)^3, which is 1a^3 + 3a^2b + 3ab^2 + 1b^3.
Pascal's triangle has many applications in mathematics, including in combinatorics, probability, and binomial theorem. It also has connections to other mathematical concepts such as Fibonacci sequence and the Sierpinski triangle.
Pascal's triangle has an infinite number of rows, as it can continue to be expanded infinitely by following the pattern of adding the two numbers above to get the next number in the row.
The sum of the numbers in each row of Pascal's triangle is equal to 2^n, where n is the row number. For example, the sum of the numbers in the fifth row (1 4 6 4 1) is 2^5 = 32.