# How do you use the Harmonic Series to prove that an infinite series diverges?

You can use the Harmonic Series to prove that an infinite series diverges by showing that its terms do not approach zero. The Harmonic Series is the sum of the reciprocals of positive integers. Mathematically, it is represented as (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \cdots).

By comparing each term of the series to the corresponding term of the Harmonic Series, if the series being tested has terms that are greater than or equal to the terms of the Harmonic Series, then it also diverges.

The divergence of the Harmonic Series can be shown using various methods such as the integral test, comparison test, or limit comparison test. These methods demonstrate that the series does not converge and hence diverges.

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Since the harmonic series is known to diverge, we can use it to compare with another series. When you use the comparison test or the limit comparison test, you might be able to use the harmonic series to compare in order to establish the divergence of the series in question.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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- How do you determine if #a_n(1+1/sqrtn)^n# converge and find the limits when they exist?
- How do you determine if the improper integral converges or diverges #int 3/(7x^2 +4) # from negative infinity to infinity?

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