Is this series convergent or divergent?

[fball558]

convergent or divergent??

Homework Statement

i took a calc 2 quiz today and had a question on one of the. it's too late to correct what i did, but it's never too late to learn it for the final haha

here is the problem
they want us to find the sum of the series (below) from 1 to infinity (i don't know how to code it so will try my best to represent it)

inf
E (-1)^n * n/(3n +1)
1


i need to find if it is conv or div.
i jumped straight to test of divergence which states that if the limit of the the function as it approaces infinity of (An) "function" does not approach 0 then it div. i know limit of the
n/3n+1 is 1/3 so i said that the function diverges but did not know what the (-1)^n did. would that change it any? or was i right?

 

[HallsofIvy]

Then look at that test again. Does it say what sign the numbers must be? If I recall correctly, it does not so the (-1)ⁿ does not matter.