I came across a problem in my homework to construct a MacLaurin polynomial of the nth degree for [tex]\sqrt{1+x}[/tex], and had some major problems. I gave up and looked up the answer on the internet, which was fairly complex: [tex]\sum \frac{(-1)^{n}(2n)!x^{n}}{(1-2n)(n!)^{2}(4^{n})}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Well, I know I couldn't have come up with that myself right now (unless I spent much more time trying to figure it out than I want to), so are there any "tricks" or strategies for coming up with MacLaurin polynomials like this that aren't intuitive?

The only way I know of constructing the polynomials is to work my way from the first term of the MacLaurin polynomial, to the second, ..., and then look for an obvious pattern to create a general formula. This pattern was not obvious to me at all; with the (2n)!, (n!)^2, 4^n, and all that. How the hell am I supposed to guess that, lol.

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# Strategies for constructing Maclaurin polynomials?

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