Especially since it's probably the easiest test.micromass said:Correct! A good advice: Always apply the test for divergence first!
The series arctan n is a mathematical series that represents the arctangent function, which is the inverse of the tangent function. It is written as Σ arctan n = arctan 1 + arctan 2 + arctan 3 + ... + arctan n.
In order for the series arctan n to converge, the limit of the series as n approaches infinity must exist and be a finite number. This can be determined by using various convergence tests, such as the Ratio Test or the Comparison Test.
The series arctan n converges conditionally, meaning that it converges but not absolutely. This can be shown by using the Alternating Series Test, which states that if a series alternates in sign and the absolute value of its terms decreases, then the series converges conditionally.
The value of the series arctan n when it converges is approximately 1.5708 radians or 90 degrees. This can be determined by using the formula for the arctangent function, which is arctan x = tan-1 x.
Yes, the series arctan n can be divergent. This would occur if the limit of the series as n approaches infinity does not exist or is infinite. In this case, the series would not converge and would be considered divergent.