What about the following sequence?

If we take quotients of entries in the last row instead of differences,
we see that every quotient is 4. So *f*''(*n*) is a geometric, not an
arithmetic sequence (as in our earlier examples).

What is the ``antiderivative'' of ? Maybe we can figure this out if we can determined the ``derivative'' of .

So the ``antiderivative'' of is .

Now we can find a formula for the sequence.

This method works in general if is geometric.

Wed Jan 6 11:37:02 EST 1999