Real Sequence/Examples/n over (n+1)

Examples of Real Sequence
The real sequence $S$ whose first few terms are:


 * $\dfrac 1 2, \dfrac 2 3, \dfrac 3 4, \dotsc$

can be defined by the formula:
 * $S = \sequence {\dfrac n {n + 1} }_{n \mathop \ge 1}$

$S$ is strictly increasing.

Proof
Let $s_n$ denote the $n$th term of $S$.

We have:

Hence $S$ is increasing by definition.