Question

Determine the limit of the following sequence, or state that it diverges.

Answer 1

hint:
we have the subsequent limit:
\[\huge \mathop {\lim }\limits_{n \to \infty } \sqrt[n]{n} = 1\]

Answer 2

furthermore we can rewrite your sequence as follows:
\[\huge {a_n} = {\left( {\sqrt[n]{n}} \right)^3}\]

Answer 3

so find the vaule of an

Answer 4

?

Answer 5

Limit goes to 1. I graphed it and it slowly converges to 1.