Question

Determine whether the following series converge or diverge. Justify your answer, stating the name of the test you use, showing why you can use it, and how the test applies. 1. $1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125} + ...$ 2. $\frac{1}{2} + \frac{1}{5} + \frac{1}{8} + \frac{1}{11} + \frac{1}{14} + ...$ 3. $\sum_{n=1}^{\infty} \frac{cos^2 n}{n^5 + 2}$ 4. $\sum_{n=1}^{\infty} \frac{\sqrt{n} + 5}{n^2}$ 5. $\sum_{n=1}^{\infty} sin(\frac{1}{n^4})$ 6. $\sum_{n=1}^{\infty} \frac{n + 6}{n\sqrt{n}}$

          Determine whether the following series converge or diverge. Justify your answer, stating the name of the test you use, showing why you can use it, and how the test applies.
1. $1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125} + ...$
2. $\frac{1}{2} + \frac{1}{5} + \frac{1}{8} + \frac{1}{11} + \frac{1}{14} + ...$
3. $\sum_{n=1}^{\infty} \frac{cos^2 n}{n^5 + 2}$
4. $\sum_{n=1}^{\infty} \frac{\sqrt{n} + 5}{n^2}$
5. $\sum_{n=1}^{\infty} sin(\frac{1}{n^4})$
6. $\sum_{n=1}^{\infty} \frac{n + 6}{n\sqrt{n}}$

Determine whether the following series converge or diverge. Justify your answer, stating the name of the test you use, showing why you can use it, and how the test applies.
1. 1 + (1)/(8) + (1)/(27) + (1)/(64) + (1)/(125) + ...
2. (1)/(2) + (1)/(5) + (1)/(8) + (1)/(11) + (1)/(14) + ...
3. ∑n=1^∞(cos^2 n)/(n^5 + 2)
4. ∑n=1^∞(√(n) + 5)/(n^2)
5. ∑n=1^∞ sin((1)/(n^4))
6. ∑n=1^∞(n + 6)/(n√(n))

Added by James R.

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