# List of Notes - Category: Monotonic Sequence

## Monotonic Sequence Definition

Sequence x_n is called increasing if x_1<x_2<...<x_n<x_(n+1)<..., i.e. if n'>n then x_(n')>x_n.

For example, {1,2,3,6,7,9,...} is increasing sequence, while {3,5,8,1,5,6,7,...} is not.

## The Euler Number e

Now let's consider sequence x_n=(1+1/n)^n and try to find its limit.

It is not very clear whether this sequence is monotonic or not.

So, to make sure that this sequence is increasing let's rewrite sequence using binom of Newton with a=1 and b=1/n: