I understand how this works:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\cos x = \frac{1}{0!} - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \frac{x^{10}}{10!} + \ldots[/tex]

But what about this?

[tex]\frac{1}{\cos x} = \frac{1}{0!} + \frac{x^2}{2!} + \frac{5x^4}{4!} + \frac{61x^6}{6!} + \frac{1385x^8}{8!} + \frac{50521x^{10}}{10!} + \ldots[/tex]

Is there a way to take the reciprocal of an infinite series or is it necessary to take subsequent derivatives of secant and write the Taylor expansion that way?

Thanks,

Unit

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# Secant series

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