How do you use the Integral test on the infinite series #sum_(n=1)^oo1/sqrt(n+4)# ?
Since the integral
diverges, the series
also diverges by Integral Test.
Let us evaluate the integral.
by the definition of improper integral,
by taking the antiderivative,
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To use the Integral Test on the infinite series (\sum_{n=1}^\infty \frac{1}{\sqrt{n+4}}), follow these steps:

Formulate the corresponding integral: ( \int_{1}^{\infty} \frac{1}{\sqrt{n+4}} , dn).

Evaluate the integral.

Determine if the integral converges or diverges.

If the integral converges, then the series (\sum_{n=1}^\infty \frac{1}{\sqrt{n+4}}) converges. If the integral diverges, then the series also diverges.
So, for the given series, you'd integrate ( \frac{1}{\sqrt{n+4}} ) from 1 to infinity and analyze the result to determine whether the series 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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