Determine whether the following series converges or diverges

Determine whether the following series converges or diverges: sigma k=0 to infinity (-1)^k^ksquareroot5

Solution

We know that Lim a_n 0 , then a_n diverges.

n--->

Hence,

Lim (-1)^k (5)^1/k = oscillating between -1 and +1 0

k----->

Hence,

Given series is diverges.