Image: Wikimedia Commons

Edric Cane came up with a simple way to establish any row in Pascal’s triangle, creating a simple sequence of fractions that, when multiplied successively, will produce the numbers in any desired row. Here’s an example for Row 7, giving the coefficients for (a + b)7 = a7 + 7a6b + 21a5b2 + 35a4b3 etc.:

triangle calculator - row 7

Another example, for Row 10:

triangle calculator - row 10

The same can be done for any desired row.

(Thanks, Alex.)

from Futility Closet