Hello, Bruce!

I'll try to explain the routine that I was taught . . .Say i have the continued fraction: .

How do i calculate it's convergents?

The solution has a table which reads as follows

Column 1 is obviously the continued fraction.

Where do the convergents come from?

Place the numbers in arowof a horizontal chart.

The table looks like this:

The rows can be completed with this strange move . . .

This is from: .

The next comes from:

From: .

The rows are filled with an identical move . . .

From: .

Then:

From: .

And the table can be completed:

The convergents are of the form:

The convergents are:

. .

. .

Note that the convergents are alternately above and below

. . the exact value of: .