# Practice Problems for Module 8

Section 11.3

Directions. The following are review problems. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. You can also follow the link for the full video page to find related videos.
1. Consider: $$\displaystyle \sum_{n=1}^\infty 3n^2e^{-n^3}$$
1. Show that the series converges.
2. Estimate the maximum error involved by approximating the sum of the series using the first eight terms.
3. How many terms are equired to estimate the sum of the series within an error of $$e^{-27}$$?

1. Converges to $$e^{-1}$$
2. bounded above by $$e^{-512}$$
3. only 3 terms
Video Errata: Before using the integral test, you must make sure that the function is continuous, positive, and decreasing.

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