Hello, max17!

Here is some of it . . .

Describe how to find the numerator of the sixth row.

Using technology, plot the relation between the row number, n, and the numerator in each row.

Describe what you notice from your plot and write a general statement to represent this.]

The numerator of the row is the Triangular Number: .

Find the sixth and seventh rows. . Describe any patterns you used.

Let E_n(R) be the (r+t)^th element in the n^th row, starting with r=o.

What isR? . . . What isr? . . . What ist?

I believe they are:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here is my reasoning . . .

Read down the "first" diagonal.

The denominators are:

This is a quadratic function:

The next two denominators are:

Read down the "second" diagonal.

The denominators are:

This is a quadratic function:

The next two denominators are:

Read down the "third" diagonal.

The denominators are:

This is a quadratic function:

The next two denominators are: