Question

Use the Growth Rates of Sequences Theorem to find the limit of the following sequence or state that they diverge. {eq}{n^{16}/(\ln n)^{32}} {/eq}

Select the correct choice below and, if necessary, fill in the answer box to complete the choice
A. The limit of the sequence is___________ . (Simplify your answer.)
B. The sequence diverges____________.

Answer 1

The sequence diverges ( B )

Step-by-step explanation:

`(n^(16) )/((In n)^(32) )`

Applying the Growth rates of sequences theorem to find the limit of the given sequence above

`\lim_(n \to \infty) (n^(16) )/((In n)^(32) )` = ∞ this means that

The sequence is divergent because the rate at which n increase is very much higher than the rate at which (In n) increases