The Integral Test and P Series Worksheet with Answer Key

What's on the worksheet

1. Write each term as Cn^p for a constant C, name p, and decide whether the series converges by the p-series test.
   \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{\sqrt{n^3}}\displaystyle\sum_{n=1}^{\infty} n^{-2/3}\displaystyle\sum_{n=1}^{\infty} \dfrac{n^2}{\sqrt[3]{n^7}}\displaystyle\sum_{n=1}^{\infty} \dfrac{4}{n\sqrt[4]{n}}\displaystyle\sum_{n=1}^{\infty} \dfrac{\sqrt[5]{n^2}}{n\sqrt{n}}
2. Use the integral test.
   \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n(1 + \ln n)}\displaystyle\sum_{n=1}^{\infty} \dfrac{\arctan n}{1 + n^2}
3. Consider the series below, and let $f
4. Let S_N = _n=1^N 1[4]n.
5. The series _n=1^∞ 1n² + 1 has a sum S known to be about 1.076674.
6. Consider the series below, where p is a real number.