MathDB

[asy] label("

1

",(0,0),S); label("

1

",(-1,-1),S); label("

1

",(-2,-2),S); label("

1

",(-3,-3),S); label("

1

",(-4,-4),S); label("

1

",(1,-1),S); label("

1

",(2,-2),S); label("

1

",(3,-3),S); label("

1

",(4,-4),S); label("

2

",(0,-2),S); label("

3

",(-1,-3),S); label("

3

",(1,-3),S); label("

4

",(-2,-4),S); label("

4

",(2,-4),S); label("

6

",(0,-4),S); label("etc.",(0,-5),S); //Credit to chezbgone2 for the diagram[/asy]
Pascal's triangle is an array of positive integers(See figure), in which the first row is

1

, the second row is two

1

's, each row begins and ends with

1

, and the

k^\text{th}

number in any row when it is not

1

, is the sum of the

k^\text{th}

and

(k-1)^\text{th}

numbers in the immediately preceding row. The quotient of the number of numbers in the first

n

rows which are not

1

's and the number of

1

's is

<span class='latex-bold'>(A) </span>\dfrac{n^2-n}{2n-1}\qquad<span class='latex-bold'>(B) </span>\dfrac{n^2-n}{4n-2}\qquad<span class='latex-bold'>(C) </span>\dfrac{n^2-2n}{2n-1}\qquad<span class='latex-bold'>(D) </span>\dfrac{n^2-3n+2}{4n-2}\qquad <span class='latex-bold'>(E) </span>\text{None of these}

Problem Statement