I saw a really great study guide that got passed around before the first Engineering 195 test, so I thought it would be a great idea to create a collaborative study guide for MA 181.

**Convergent and Divergent Series Tests**

1. The nth-Term Test:

Unless $ a_{n}\rightarrow 0 $, the series diverges

2. Geometric series:

$ \sum_{n=1}^\infty ar^n $ converges if $ |r| < 1 $; otherwise it diverges.

3. p-series:

$ \sum_{n=1}^\infty 1/n^p $ converges if $ p>1 $; otherwise it diverges

4. Ratio Test(for series with non-negative terms):

$ \lim \limits_{n \to \infty }{\frac{a_{n+1}}{a_{n}}}=p $ The series converges if p<1, diverges if p>1, and is inconclusive if p=1

5. Root Test(for series with non-negative terms):

$ \lim \limits_{n \to \infty }{\sqrt[n]{a_{n}} }=p $ The series converges if p<1, diverges if p>1, and is inconclusive if p=1

More to come...

I am looking to check my answers to the practice problems that Dr. Bell posted on our home page, so if someone would please post them I would really appreciate it. Gleenhee 20:10, 17 November 2008 (UTC)

That's a lot to post. Are there any that you are just not sure about? --Ctuchek 19:31, 18 November 2008 (UTC)