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) multiplied by
a constant:
Since for n ³ 1
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|
arctan(n)
n2+1
|
£ |
p/2
n2+1
|
£ |
p
2
|
|
æ
ç
è
|
|
1
n2
|
|
ö
÷
ø
|
|
|
then the implies convergence of the series.
Note that this problem can also be solved using the Integral Test and
Limit Comparison Test.