I cannot get the Auto Fill function to increase values in a series, and I
feel certain I'm doing it right:

First, I tried typing a series of values in a column like this: Cell A1, I
typed 1. Cell B1, I typed 2. Then, I selected both cells with the mouse, and
then moved to the lower right corner of Cell B1 and left-clicked and held the
mouse button down. Then I dragged the mouse button down several columns. The
little pop-up message seemed to indicate that it was repeating 1, 2, 1, 2.
When I released the mouse button, it had actually filled a 1 in each cell!

After several unsuccessful attempts, I read online help and decided to try
using a different method: the Fill tool function button on the toolbar. I
could not seem to make that command work.

The instructions in Online Help suggested I had a problem. I read, "1. On
the Home tab, in the Editing Group, click Fill, and then click Series." When
I clicked Fill, the Series command was grayed out, apparently regardless of
what I had selected: a blank cell, a series of cells with a series of
increasing values, or a combination of both.

I began to suspect that my program settings were "messed up", so I clicked
the Microsoft Office button, then the Excel Options button near the bottom
right corner of the tab, as it instructed. I reviewed all the settings.
Everything appears to be set properly. For example, Under Advanced options,
"Enable fill handle and cell drag-and-drop" is checked, as is almost every
other option on that tab.

I wondered if there was an configuration problem with my software, so I even
ran the online Microsoft Office Diagnostics. It found no problems, conflicts,
etc.

What am I doing wrong?