Beck said "show us what you showed me in my office" implying that he'd been shown the problem before.

But it should be fairly obvious to any calculus student that that series doesn't converge since the limit as it goes to infinity isn't 0... It doesn't even exist. Sine and cosine functions are an immediate red flag to this, all you need to do to look at it is a simple order of magnitude analysis.

Nevertheless, I'm sure he's very smart. But I'm not sure he has much common sense if he didn't see that right away. I'll also echo Alex's sentiments below...