Todd's Evil Limit

One day colleague my colleague, Todd, walked into my office and showed this to me:

I shared this bit of villany with the AP calculus mailing list, and received several questions about it. Here are the answers:

1) Todd found this as an exercise in "Excursions in Calculus" by Robert M. Young. He recommends that all of you read this book.
2) The reason that your calculator gives you wild answers is that the n factorial grows very large, very quickly. When you take the sine of a number, you really are interested in that number's value modulo 2*PI. The size of n factorial makes that latter calculation impossible, so you wind up with pretty much random numbers.
3) Todd is not single. Sorry.
4) If you want a hint in proving this limit, click here.

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