Is this series convergent or divergent?

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SUMMARY

The series in question is defined as the sum from 1 to infinity of the terms (-1)^n * n/(3n + 1). The initial analysis using the test for divergence indicates that the series diverges since the limit of the term n/(3n + 1) approaches 1/3 as n approaches infinity, which is not zero. However, the presence of the alternating factor (-1)^n suggests the need for further analysis, specifically the Alternating Series Test, which could potentially indicate convergence despite the divergence found in the initial test.

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fball558
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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?
 
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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.
 

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