Calculus II, Fall 2013

Quiz 1

Mar 07, 2013

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1. For what value of p > 0 is the improper integral ∫_{0}^{∞} \frac{1}{x^{p}} dx convergent? Explain.

2. State (need not prove) the integral test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

3. State (need not prove) the ratio test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

4. State (need not prove) the root test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test. The examples in the last 3 questions need not be different.

5. Is the series ∑_{n=1}^{∞} \frac{1}{n\sqrt[n]{n}} convergent? Explain.

Calculus II, Fall 2013

Quiz 1

Mar 07, 2013

Show all details.

1. For what value of p > 0 is the improper integral ∫_{0}^{∞} \frac{1}{x^{p}} dx convergent? Explain.

2. State (need not prove) the integral test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

3. State (need not prove) the ratio test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test.

4. State (need not prove) the root test for series with positive terms (a_{n} > 0). Then give an example of a series that can be found convergent using this test. The examples in the last 3 questions need not be different.

5. Is the series ∑_{n=1}^{∞} \frac{1}{n\sqrt[n]{n}} convergent? Explain.