(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Power series representation, I really need help!!! :-]

please let me know if i did this correctly

[tex]f(x)=\arctan{(\frac{x}{3})}[/tex]

[tex]f'(x)=\frac{\frac{1}{3}}{1-(-\frac{x^2}{3^2})}[/tex]

[tex]\frac{1}{3}\int[\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{2n}}{3^{2n}}]dx[/tex]

[tex]\frac{1}{3}\int[1-(\frac{x}{3})^{2}+(\frac{x}{3})^{4}-(\frac{x}{3})^{6}+(\frac{x}{3})^{8}+...]dx[/tex]

[tex]\frac{1}{3}[C+x-\frac{(\frac{x}{3})^{3}}{3}+\frac{(\frac{x}{3})^{5}}{5}-\frac{(\frac{x}{3})^{7}}{7}+\frac{(\frac{x}{3})^{9}}{9}][/tex]

[tex]C+\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{2n+1}}{3^{2n+1}(2n+1)}[/tex]

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# Homework Help: Power series representation, I really need help :-]

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