Improving the Convergence of Newton's Series Approximation for e

@article{Brothers2004ImprovingTC,
  title={Improving the Convergence of Newton's Series Approximation for e},
  author={Harlan J. Brothers},
  journal={The College Mathematics Journal},
  year={2004},
  volume={35},
  pages={34 - 39}
}
Harlan Brothers (hjb@thecountryschool.org) is Director of Technology at The Country School in Madison, Connecticut, where he teaches programming, fractal geometry, robotics, and jazz band. He is currently involved in integrating the study of fractals into standard mathematics curricula through his work with Michael Frame and Benoit Mandelbrot at Yale University. He is also an inventor, holding five U.S. patents. On weekends, he can often be found playing guitar in the New Haven area with the 12… 
Classroom Capsules
There is a classic puzzle called Traffic Jam at [1], which involves interchanging two sets of objects on a line by a sequence of jumps and slides. This makes a particularly nice game for elementary
96.20 Pascal's triangle: The hidden stor-e
shallow diagonal before that one. So the sum of any shallow diagonal (from the third onwards) is the sum of the two previous shallow diagonals, giving the inductive definition F" = Fn _ 1 + Fn _ 2

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