Part 7/8:
Using limit laws, we can show that as ( x ) approaches infinity, ( \frac{1}{x^r} ) approaches 0. This conclusion can also be represented within the context of sequences by substituting ( n ) for ( x ) as follows:
[
\text{limit as } n \to \infty \text{ of } \frac{1}{n^r} = 0
]
This indicates that for any rational number ( r ) greater than zero, the limit of this sequence converges to zero as ( n ) approaches infinity.