5 questions 29

Please see the attachment, it has all 5 questions.


Determine its convergence by integral test.



∑𝑛=1∞arctan(𝑛)𝑛2+1




∑



n


=


1




∞






arctan


⁡


(


n


)





n


2



+


1




1) List the conditions that allow integral test.

2) Perform integral test appropriately.

3) State your conclusion about the series.

Hint:

∫arctan(𝑥)1+𝑥2𝑑𝑥=(arctan(𝑥))22+𝐶

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