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Power series for the inverse tangent
The power series for the inverse tangent is
Explanation
The first derivative of the inverse tangent is
We differentiate this several times
The point x = 0 gives
We substitute this in the Taylor series and find
so
General format
You can write the power series as a sum
It converges too slowly to be able to use in practice.
Example 1
You can see that tan-1(0) = 0, because
tan-1(0) = 0 − 0 + 0 − ... = 0