What is row 1 in Pascals triangle?

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Answer 1 · 2015-07-15T22:32:13

Row 1 in Pascal's triangle consists of the single term $1$ $1$

The $n$ $n$ th row of Pascal's triangle is:

$((n-1),(0))$ $((n-1),(1))$ ... $((n-1),(n-1))$

or if you prefer:

$((n-1)!)/(0!(n-1)!)$ $((n-1)!)/(1!(n-2)!)$ ... $((n-1)!)/((n-1)!0!)$

The 1st row just consists of

$((0),(0))$

or if you prefer:

$(0!)/(0!0!)$

Now $0! = 1$ , hence $((0), (0)) = 1$

Answer 2 · 2015-07-16T14:44:36

I use the same counting as George C. The first row is row 1 and it is 1. However . . .

I have seen treatments that call the first row, "Row 0"

In that terminology, Row 1 is: $1$ $1$

(and Row 2 is: $1$ $2$ $1$ )

I assume that the reason for this is that it allows us to say that "Row $n$ gives the coefficients of $(a+b)^n$ ".