To prove that \(\lim_{n \to \infty} \frac{1}{n^{6/5}} = 0\), you can use the fact that the denominator (n raised to a positive power) increases without bound as n approaches infinity.
Here's a brief proof:
Given the limit expression: \(\lim_{n \to \infty} \frac{1}{n^{6/5}}\)
As \(n\) approaches infinity, the denominator \(n^{6/5}\) becomes larger and larger. In the limit, the fraction \(\frac{1}{n^{6/5}}\) approaches zero because you are dividing 1 by an increasingly larger number.
So, \(\lim_{n \to \infty} \frac{1}{n^{6/5}} = 0\).