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Topic: Convergence arctan taylor searies
Replies: 1   Last Post: Feb 20, 2013 7:35 PM

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Dave Rudolf

Posts: 37
Registered: 10/3/05
Convergence arctan taylor searies
Posted: Feb 20, 2013 7:04 PM
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Hey folks,

I was looking at the taylor series that is commonly used to compute
arc-tangent, which is

atan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9....

However, the domain for arc-tangent is +/- infinity. So, for x values
that are a bit larger than 1 (or smaller than -1), I don't see how
this series converges to anything. For instance, if I did atan(2),
then (2)^n will grow a lot faster than n itself, so each term will be
larger than the last.

Or am I missing something here?

Thanks.

Dave



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