Thoughts on Infinity: Index

Calculus, Precalculus 1 Minute

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on various lessons I’ve learned while trying to answer the questions posed by gifted elementary school students.

Part 1: Different types of countable sets

Part 2a: Divergence of the harmonic series.

Part 2b: Convergence of the Kempner series.

Part 3a: Conditional convergent series or products shouldn’t be rearranged.

Part 3b: Definition of the Euler-Mascheroni constant \gamma.

Part 3c: Evaluation of the conditionally convergent series \displaystyle 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} \dots

Part 3d: Confirmation of this evaluation using technology.

Part 3e: Evaluation of a rearrangement of this conditionally convergent series.

Part 3f: Confirmation of this different evaluation using technology.

Part 3g: Closing thoughts.

 

Published by John Quintanilla

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.

Published

18 thoughts on “Thoughts on Infinity: Index”

  1. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 1 | Mean Green Math
  2. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 2 | Mean Green Math
  3. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 3 | Mean Green Math
  4. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 4 | Mean Green Math
  5. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 5 | Mean Green Math
  6. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 6 | Mean Green Math
  7. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 7 | Mean Green Math
  8. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 9 | Mean Green Math
  9. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 10 | Mean Green Math
  10. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 11 | Mean Green Math
  11. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 12 | Mean Green Math
  12. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 13 | Mean Green Math
  13. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 14 | Mean Green Math
  14. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 15 | Mean Green Math
  15. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 16 | Mean Green Math
  16. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 17 | Mean Green Math
  17. Pingback: What I Learned from Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Part 18 | Mean Green Math
  18. Pingback: What I Learned by Reading “Gamma: Exploring Euler’s Constant” by Julian Havil: Index | Mean Green Math

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