2011-07-05, 08:22 AM
Stolen Wikipedia Images
How does one show that the two expansions are equal, without first proving that they're equal to the exponential function (eg. using algebraic manipulations (multiplication?) or calculus tricks)?![[Image: 7d55313dd5b2370831cc6db.png]](http://img813.imageshack.us/img813/2782/7d55313dd5b2370831cc6db.png)
![[Image: 2b8f73649758a53d36c2ed5.png]](http://img215.imageshack.us/img215/255/2b8f73649758a53d36c2ed5.png)
Also, why aren't continued functions used much in practice to approximate functions? How does one derive a continued fraction expansion of a function, and how does one determine the error term on such an expansion? I really don't understand where continued fractions come from, so can someone please break it down in understandable terms for me?
