Calculus II, Spring 2016

Quiz 1

Mar 03, 2016 Show all details.

1. Give formal definition of lim_{n→∞} a_{n} = L

2. Is ∫0^{\frac{π}{2}} \sqrt{tan t} dt convergent? Explain.

3. Is ∑_{n=1}^{∞} (1 + \frac{1}{n})^{n} convergent? Explain.

4. Is ∑_{n=3}^{∞} \frac{1}{n(ln n)^{2}} convergent? Explain.

5. Is ∑_{n=1}^{∞} \frac{1}{\sqrt{n^{3} + 1}} convergent? Explain.

6. Is ∑_{n=1}^{∞} \frac{2^{n}n!n!}{(2n)!} convergent? Explain.

Calculus II, Spring 2016

Quiz 1

Mar 03, 2016 Show all details.

1. Give formal definition of lim_{n→∞} a_{n} = L

2. Is ∫0^{\frac{π}{2}} \sqrt{tan t} dt convergent? Explain.

3. Is ∑_{n=1}^{∞} (1 + \frac{1}{n})^{n} convergent? Explain.

4. Is ∑_{n=3}^{∞} \frac{1}{n(ln n)^{2}} convergent? Explain.

5. Is ∑_{n=1}^{∞} \frac{1}{\sqrt{n^{3} + 1}} convergent? Explain.

6. Is ∑_{n=1}^{∞} \frac{2^{n}n!n!}{(2n)!} convergent? Explain.