Math 6B
Worksheet 8
Winter 2025
Due Thursday, Feb 27, at 11:59pm.
This worksheet is meant as a review of infinite series, which you should be familiar with from Math 3B. Review power series, alternating series, telescopic series, basic divergence test, root test, ratio test, integral test, Taylor series, . . . .
1. Give an example of a series Σan, where an → 0 as n → ∞ , but Σan diverges.
2. Evaluate the following series.
3. Determine the convergence or divergence of the following series.
4. are given. Use these and the root test to show the convergence or divergence of
5. Write the Taylor series for the following functions.