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I'm lost, and my textbook is failing me
2026-04-07 00:47:30.1775522850
Series -- Coefficient Cn and Radius of Convergence
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To identify the $c_n$, look up the definition of MacLaurin series. This will tell you how $c_n$ relates to $f^{(n)}(0)$.
To figure out the radius of convergence, fix $x$ and use the ratio test. This will give you $|x|<R$. (You have to figure out $R$.) After you do this, substitute $x = R$ and $x=-R$ into the series to determine whether or not the MacLaurin series converges at the endpoints of the interval of convergence.