Use the Root Test to determine the convergence or divergence of the series.

$1\frac{2}{7}\frac{3}{7^2}\frac{4}{7^3}\frac{5}{7^4}\frac{6}{7^5}$ cdots

Evaluate the following limit$.$

$\underset{n}{lim}\sqrt[n]{|a_n|}$

$$

Determine the convergence or divergence of the series. Explain your reasoning.

The series converges by the Root Test. The limit of the $n^{th}$ roots of terms is less than $1.$

The series diverges by the Root Test. The limit of the $n^{th}$ roots of terms is greater than $1.$

The series diverges by the Root Test. The limit of the $n^{th}$ roots of terms is equal to $1.$