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I'm trying to find the first five terms of a Maclaurin series using division.

Is there possibly a shorter way because every time I try to do it for $$\frac{\sin x}{e^x}$$

I get the wrong answer: $x-2x^3/3+\cdots$

I don't really like polynomial long division.

This is how I set it up:

x - x^3/3! + x^5/5! - x^7/7! ÷ 1 + x + x^2/2! + x^3/3! + x^4/4!

I'm still getting the same answer.

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    Either you divide, or you compute the series by computing the derivatives of $\sin x/e^x$ directly. The series does not start like you say it does, so your computation is wrong. In any case, "I don't really like polynomial long division" is not exactly motivation...2011-03-28
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    I've tried long division and that's the answer I get.2011-03-28
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    Well, you are doing it wrong, then! The series for that function starts $x - x^2 + x^3/3 + \cdots$ By the way, why do you think the result you get is *weird*?2011-03-28
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    @Mariano Suárez-Alvarez: Because it's not the right answer.2011-03-28
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    Oh. You could probably edit the body of the question to replace *weird* by *wrong*, which is much more clear :)2011-03-28
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    In your setup you divide $\frac{e^x}{\sin{x}}$...2011-03-28
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    How did you get your answer Mariano Suárez-Alvarez?2011-03-28

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