Choosing a Convergence Test Worksheet with Answer Key

What's on the worksheet

1. Decide whether each series converges or diverges.
   \sum_{n=1}^{\infty} \dfrac{n^2 + 1}{\sqrt{n^4 + 3}}\sum_{n=1}^{\infty} \dfrac{n^n}{3^{n^2}}\sum_{n=1}^{\infty} \dfrac{n^3\, 4^n}{(n+1)!}\sum_{n=1}^{\infty} \dfrac{1}{n\left(1 + (\ln n)^2\right)}
2. Classify each series as absolutely convergent, conditionally convergent, or divergent.
   \sum_{n=1}^{\infty} (-1)^n \dfrac{n^3}{2^n}\sum_{n=1}^{\infty} (-1)^{n+1} \left(\sqrt{n+1} - \sqrt{n}\right)\sum_{n=1}^{\infty} (-1)^n \dfrac{\sin^2 n}{n^2}\sum_{n=1}^{\infty} (-1)^n \dfrac{3^n}{3^n + n^3}
3. Let S be the sum of the series below, if it exists.
4. Consider the series below.
5. Consider the series below.
6. For each description, give a series that fits it and show that it does, or explain why no series can fit it.