Test the series for convergence or divergence using the Alternating Series Test.

$(1)$n$1$bnn $=1$

$=$

$1$

$2$

$$

$1$

$3$

$+$

$1$

$4$

$$

$1$

$5$

$+$

$1$

$6$

$$

Identify

bn$.$

Evaluate the following limit$.$

$$lim$$n$$$$bn$$