# LaGrange Error and power series

1. Mar 15, 2007

### SoaringQuail

There's a homework problem that I've been struggling over:

Find a formula for the truncation error if we use 1 + x^2 + x^4 +x^6 to approximate 1/(1-x^2) over the interval (-1, 1).

Now, I assume that you need to use LaGrange error but I'm not sure how to proceed. Any help would be greatly appreciated.

2. Mar 15, 2007

### HallsofIvy

Staff Emeritus
Since you mention LaGrange error, presumably you know the formula for it! Off the top of my head, I believe it is
$$E\le \frac{M}{(n+1)!}|x-a|^{n+1}$$
where M is an upper bound on the n+ 1 derivative. Here, by the way, you can take either n+1= 7 or replace "x2" by "y" and use n+1= 4 with the formula in y.

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