## 3.1. Sequences

### Example 3.1.3(c):

*{ n / 2 ^{n} } = { 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

forn^{2}2^{n}

*n > 3*. But then we have that

or equivalentlyn^{2}/ 2^{n}1

forn / 2^{n}1/n

*n > 3*. But now you should be able to finish the proof yourself. As a hint, for a given , choose

N = max{3, 1/}