# How do you show that the harmonic series diverges?

The harmonic series diverges, which means its sum approaches infinity as you add more terms. This can be shown using the integral test or by comparing it to other known divergent series, such as the series of reciprocals of natural numbers. The integral test involves comparing the series to the integral of 1/x from 1 to infinity, which diverges logarithmically. Alternatively, you can demonstrate divergence by grouping terms in the series into sets, such as powers of 2, and showing that each set sums to a value greater than 1.

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Since the above shows that the harmonic series is larger that the divergent series, we may conclude that the harmonic series is also divergent by the comparison test.

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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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