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how could i expand something such as arctan'x into a power series. also how would you be able to find the power series for it?

so far i have managed to work out that:

arctan'x = [itex] \frac{1}{1 + x^2} [/itex]

[itex]\frac{1}{1+x^2} = 1 - x^2 + x^4 - x^6 +...+ (- 1)^n x^{2n}[/itex]

how do you work out the radius of convergence though: i know it is : |x|< 1.. but how do you work it out please?

so far i have managed to work out that:

arctan'x = [itex] \frac{1}{1 + x^2} [/itex]

[itex]\frac{1}{1+x^2} = 1 - x^2 + x^4 - x^6 +...+ (- 1)^n x^{2n}[/itex]

how do you work out the radius of convergence though: i know it is : |x|< 1.. but how do you work it out please?

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