The discussion revolves around finding an equation to predict the middle number in Pascal's triangle, specifically focusing on rows with an odd number of elements. Participants explore examples and seek clarification on the definition of the "middle number."
Participants express a common interest in identifying the middle number, but there is no consensus on a specific equation or method to predict it. Multiple viewpoints and approaches are presented without resolution.
Some assumptions about the definition of "middle number" and the conditions under which the equation applies remain unclear. The discussion does not resolve the mathematical steps needed to derive a specific formula.
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