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 8.3.8 (a): Power Series?

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Is the geometric series function xⁿ a power series? List its center and the radius of convergence. What is each coefficient a_n?

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Yes, the geometric series is a power series centered at c = 0 with radius of convergence r = 1. Each coefficient a_n = 1.

xn	f(x) = 1/1-x