Absolute and Conditional Convergence Worksheet with Answer Key

What's on the worksheet

1. Classify each series as absolutely convergent, conditionally convergent, or divergent.
   \sum_{n=1}^{\infty} (-1)^n \dfrac{n}{n^3 + 4}\sum_{n=1}^{\infty} (-1)^{n+1} \dfrac{n + 2}{n^2 + 3}\sum_{n=1}^{\infty} (-1)^n \dfrac{2n}{3n + 1}\sum_{n=2}^{\infty} \dfrac{(-1)^n}{n(\ln n)^2}\sum_{n=2}^{\infty} \dfrac{(-1)^{n+1}}{\sqrt{n}\,\ln n}
2. The signs of the two series below do not alternate.
3. Let S be the sum of the series below, and S_N its Nth partial sum.
4. For a series a_n, let p_n = (a_n, 0) and q_n = (-a_n, 0) be its positive and negative parts.
5. Say whether each claim is true or false, and give the reason, naming any test or fact you use.
6. Let a_n = (34)^n 2nπ3 for n ≥ 1, with positive part p_n = (a_n, 0) and negative part q_n = (-a_n, 0).