Not necessarily. There's no exception to the theorem - in fact, the infinity quantity (is that an oxymoron?) is an important part of all limits. In this example in particular, the limits of each individual function are all zeroes. In one of the few definite operations involving infinity and zero, the product is zero.

In the end, I'm just confusing myself slightly. But an infinite series doesn't mean the theorem breaks down. I said it was a paradox because for pretty much all convergent series it does hold - even at infinity. This is tricky because for each increase in n, the value decreases but the length increases.