Is the series #\sum_(n=1)^\inftyn^2/(n^3+1)# absolutely convergent, conditionally convergent or divergent?
(Use the appropriate test)
(Use the appropriate test)
1 Answer
Diverges by the Limit Comparison Test
Explanation:
Due to the simplicity of the series, we can use the Limit Comparison Test, which tells us if we have some positive sequence
Here,
For the comparison sequence, we need one whose series' convergent or divergent behavior we know. So, we'll say
Now,
So,
Thus, as both series must diverge because of this result, the series diverges by the Limit Comparison Test.
We don't need to check for absolute convergence -- if