Correct Answer!
By the :
Consider the series
|
|
¥
å
n = 1
|
| an| = |
¥
å
n = 1
|
|
arctan(n)
n2+1
|
|
|
and compare it to the convergent p-series (p=2):
Since both series have positive terms and the limit
is finite an positive then the implies convergence of the series.
Note that this problem can also be solved using the Integral Test and the
Direct Comparison Test.