# Solutions to Problem Set 17

Math 211-03

10-17-2017

[p-series]

1. Determine whether the series converges or diverges.

This is a p-series with . Hence, it diverges.

2. Determine whether the series converges or diverges.

This is a p-series with . Hence, it converges.

3. Determine whether the series converges or diverges.

Let . When , I have . So

This is a p-series with . Hence, it converges.

Note: As a shortcut, I will call series like this "p-series", even though they do not start with index 1.

[Zero Limit Test]

4. Determine whether the series converges or diverges. If the series converges, find the exact value of its sum.

The terms of the series do not go to 0. Hence, the series diverges by the Zero Limit Test.

5. Determine whether the series converges or diverges. If the series converges, find the exact value of its sum.

The terms of the series do not go to 0. Hence, the series diverges by the Zero Limit Test.

6. Determine whether the series converges or diverges. If the series converges, find the exact value of its sum.

The terms of the series do not go to 0. Hence, the series diverges by the Zero Limit Test.

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