The equation for predicting the middle number in Pascal's triangle can be derived using the binomial coefficient formula, specifically \(\frac{n!}{k!(n-k)!}\), where \(n\) is the row number and \(k\) is the position in that row. For rows with an odd number of elements, the middle number corresponds to the value at position \(k = \frac{n}{2}\). For example, in row 6, the middle number is 20, while in row 5, the middle number is 6. This pattern continues with subsequent rows, confirming the relationship between consecutive rows.
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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 \frac{n!}{k!(n-k)!}?
Svein said:And then: 924, 3432, 1287, 48620, 184756, 705432gnome222 said:numbers 2, 6, 20, 70, 252