I want to evaluate [tex] \int \frac{\sin x}{x} [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

So [tex] \sin x = \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{2n+1}}{(2n+1)!} [/tex]. Therefore [tex] \frac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{2n}}{(2n+1)!} [/tex]. So would that mean:

[tex] \int \frac{\sin x}{x} = C + \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{2n+1}}{2n+1(2n+1)!} [/tex] would be absolutely convergent (i.e. [tex] R = \infty [/tex])?

Thanks

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# Homework Help: Series problem help

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