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Power series for the inverse tangent

The power series for the inverse tangent is



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



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


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