What should I put for using the integral test to determine whether the series is convergent or divergent?
DIVERGES and DIVERGENT doesn't work.
~~~~~~~~~~~~~~~~~
DIVERGES and DIVERGENT doesn't work.
~~~~~~~~~~~~~~~~~
The series:
is divergent.
Based on the integral test, the convergence of the series:
is equivalent to the convergence of the improper integral:
Evaluate the indefinite integral:
then:
So the series is divergent.
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When using the integral test to determine whether a series is convergent or divergent, you should follow these steps:

Verify that the series is positive and decreasing for all terms beyond some point N.

Integrate the function represented by the series from N to infinity.

Determine whether the improper integral converges or diverges.

If the integral converges, then the series converges. If the integral diverges, then the series also 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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