# College Math Teaching

## November 21, 2013

### I am a frigging IDIOT!!!! (aka “Math Professor FAIL”)

Filed under: basic algebra, calculus, series — Tags: , , — collegemathteaching @ 5:17 pm

The topic: power series. I was showing how to manipulate the relation $\frac{1}{1-x} = \sum^{\infty}_{k=0} x^k$ to get power series of various kinds, including series centered at values other than zero. For example, if one wanted the series centered at, say, $x = 2$ we could write $\frac{1}{1-x} = \frac{1}{1-(x-2)-2} = \frac{1}{-1-(x-2)}=\frac{-1}{1-(-1)(x-2)}$ $= -\sum^{\infty}_{k=0} (-1)^k (x-2)^k = \sum^{\infty}_{k=0} (-1)^{k+1} (x-2)^k$.

And so I said: Let’s try to find the series for $\frac{1}{1-x}$ centered at $x = 1$. And. I. Was. Not. Able. To. Do. It.

So I went on to another problem…and it hit me.

O. M. G. (slamming my head on the desk here…dying of embarrassment).

Moral: never get overconfident. 🙂

Yes, I told the class of my blunder as soon as it hit me; they laughed…with me, I think. 😉