Interactive Real Analysis - part of MathCS.org

• Real Analysis
• 1. Sets and Relations
• 2. Infinity and Induction
• 3. Sequences of Numbers
• 4. Series of Numbers
• 5. Topology
• 6. Limits, Continuity, and Differentiation
• 7. The Integral
• 8. Sequences of Functions
• 8.1. Pointwise Convergence
• 8.2. Uniform Convergence
• 8.3. Series and Power Series
• 8.4. Taylor Series
• 8.5. Approximation Theory
• 9. Historical Tidbits
• Java Tools

Example 8.3.4 (e): Function Series Examples

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Does Weierstrass' theorem apply to the series we discussed previously?

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No, unfortunately that theorem does not apply - why not?

In fact, we had to expend quite a lot of energy on technical details to show that the series converges. If we did divide by n² instead of n our task would be much simpler, but the resulting function would no longer be linear.

1/n sin(nx)	1/n2 sin(nx)