What can you say about the relationship between the row number and the second term in each row in pascal's triangle?

1

1 1

1 2 1 and so on.

First row: 1. This 1 represents any nonzero base raised to power 0: b^0=1.

Second row: 1 1. These are the coefficients of a first order expression such as 1x^1 + 1x^0, or x+1.

Third row: 1 2 1 These are the coeff. of a 2nd order expression such as

1x^2 + 2x + 1 = (x+1) ^2

So it appears that the nth row contains the coefficients applying to the (n-1) th power of a binomial, such as (a+b) ^n.

If n = 3, then the 3rd row 1 2 1 contains the appropriate coeff. for the expansion of (a+b) ^ (3-1) = (a+b) ^2 = a^2 + 2ab + b^2.