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Problem 17 Medium Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence.

$ f(x) = \sinh x $

Answer

$f(x)=\sum_{n=0}^{\infty} \frac{x^{2 n+1}}{(2 n+1) !},$ $R=\infty$

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Video Transcript

Okay, So fun. The MEChA Lauren Serious forever. That's using the definition. All right, So when they use the definition to fund the McCallister's for that's so evidence because to bin from zero to infinity and conservative as zero over in editorial in experience power, so so affects is signing chess. And the problem is clothes and the Czechs again after prom because Sinan shacks and so on. So it's like alliteration. And we know that after it's zero and five times zero is this one a thumbprint Zeroes do is zero, and I've chamber prime crime. A zero is still one. So to get this clear, we can write down the definition of signing cheques and cause an Ajax. So we're plugging all this data into over equipment one, and I'm gonna have ah, that's going to be so in from Okay, So it's X class That's cute or three Victoria Plus s defied off five over material and plus so all the even number, all the terms sorry. And the finance, they're going to be okay from one to fifty. Extra power to came on this one two commanders, one pictorial site. So that's all the our terms others for the power events and the readers. Convergence is going to be the whole realign. So our O. C is just the horror line. Yes, affinity.

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