Example:
The sequence 
converges to zero.
Note that { n / 2n } = { 0, 1/2, 1/2, 3/8, 1/4, 5/32, ...}.
It is not clear, but it seems as if the terms get smaller and
smaller. Indeed, this is the case, and we will prove it:
First, we can use induction to show that
- n2
2n for n > 3
But then we have that
- n2 / 2n
1
or equivalently
n / 2n
1/n for n > 3
But now you should be able to finish the proof yourself. As a
hint, for a given 
, choose
- N = max{3, 1/}
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