How do you use the integral test to determine if #Sigma arctann/(n^2+1)# from #[1,oo)# is convergent or divergent?
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To use the integral test to determine if ( \sum \frac{\arctan(n)}{n^2 + 1} ) from ( n = 1 ) to ( \infty ) is convergent or divergent, we need to compare the given series with the corresponding integral.

Define the function ( f(x) = \frac{\arctan(x)}{x^2 + 1} ).

Check if ( f(x) ) is continuous, positive, and decreasing for ( x \geq 1 ).

If ( f(x) ) satisfies the conditions, then integrate ( f(x) ) from ( 1 ) to ( \infty ). If the integral converges, then the series also converges. If the integral diverges, then the series also diverges.

Calculate the integral ( \int_1^\infty \frac{\arctan(x)}{x^2 + 1} , dx ).

Determine whether the integral converges or diverges.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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