Convergence by Integral Test Math Questions

Convergence by Integral Test Math Questions.

Please see the attachment, it has all 5 questions.

Determine its convergence by integral test.

∑ =1∞arctan( ) 2+1

\sum_{n = 1}^{\infty} \frac{\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( )1+ 2 =(arctan( ))22+

Solution:

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