Alternating Series and Their Error Bound Worksheet with Answer Key

What's on the worksheet

1. Decide whether each series converges or diverges.
   \sum_{n=1}^{\infty} (-1)^n \dfrac{2}{\sqrt[3]{n} + 1}\sum_{n=1}^{\infty} (-1)^{n+1} \dfrac{n^2 + 1}{2n^2 - 1}\sum_{n=2}^{\infty} \dfrac{\cos(n\pi)}{n \ln n}\sum_{n=1}^{\infty} (-1)^{n+1} \dfrac{n^2}{n^3 + 50}\sum_{n=1}^{\infty} (-1)^{n+1}\, n\sin\dfrac{1}{n}
2. Let S be the sum of the series below, and S_N its Nth partial sum.
3. Lucas makes three claims.
4. Consider the series below, with Nth partial sum S_N and sum S.