How do you determine if the series the converges conditionally, absolutely or diverges given sum_(n=1)^oo (-1)^(n+1)arctan(n)∞∑n=1(−1)n+1arctan(n)?
1 Answer
Apr 13, 2018
The series diverges.
Explanation:
For
The Alternating Series Test
An alternating series
- All the
a_nan terms are positive (the sign of each term in the series alternates) - The terms are eventually weakly decreasing (
a_n>=a_(n+1)an≥an+1 for large enoughnn ) a_n->0an→0
The series fulfils the first condition of the test but fails the second condition (and third) as
And if the series doesn't converge conditionally then it doesn't converge absolutely.