In yesterday’s post, I showed that using the original definition (in terms of an area under a hyperbola) does not lend itself well to numerically approximating . Let’s now look at the other two methods.

2. The limit gives a somewhat more tractable way of approximating , at least with a modern calculator. However, you can probably imagine the fun of trying to use this formula without a calculator.

3. The best way to compute (or, in general, ) is with Taylor series. The fractions get very small very quickly, leading to rapid convergence. Indeed, with only terms up to , this approximation beats the above approximation with . Adding just two extra terms comes close to matching the accuracy of the above limit when .

More about approximating via Taylor series can be found in my previous post.

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.
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2 thoughts on “Different definitions of e (Part 12): Numerical computation”

## 2 thoughts on “Different definitions of e (Part 12): Numerical computation”