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\[ \lim_{n \rightarrow \infty} n.\sin(2\pi.e.n!) \]

|dw:1360717507664:dw|

Surprisingly, the limit does exist.

The maximum value of the sine term is unity. Therefore is the limit infinity?

No

|dw:1360795091206:dw|

What you've written is not equal to the limit in question.

just first step towords it... thinking

...and you dropped a 2pi mid way through but picked it up again; that's a small detail.

Yes

I'll tell you right now the limit is not zero.

Great.

Very surprising. Upon first glance it looks very divergent.