Calculate the limit$.$

$\underset{x}{lim}\frac{n}{\sqrt[\phantom{2}]{n^{2}14}}$

$($Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the linit does not exist.$)$

$\underset{x}{lim}\frac{n}{\sqrt[\phantom{2}]{n^{2}14}}=$

$$

Use this limit to determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n}{\sqrt[\phantom{2}]{n^{2}14}}$ conerges or diverges.

Does the series converge or diverge?

$$ Because the limit is infinite, the series diverges by the ath Form Divergence Test.

Bocause the limit is finine and nonero, the series diverges by the nat Term Divergence Test

$$ B $q,$ than $1$imit in Amiss $q,$