I am to expand $\ln(2+x)$ as a Maclaurin series, I've got that $\ln(2+x)=\sum\limits_{n=1}^{ \infty}(-\frac{1}{2})^{n}x^{n}$. Can someone check it?
Maclaurin expansion of a given function
2
$\begingroup$
calculus
sequences-and-series
power-series
1 Answers
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Your right side is a geometric progression. You know how to find the sum of one of those? And then see if it's the same as the left side?
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0The correct series will give the *exact* value of the function, not an approximation, provided you evaluate at some $x$ for which the series converges. But that's not a good way to check that you have the right series. One way to check that the answer you have given in the comments is right is to differentiate both sides. If that gives you an equality, and if in addition your answer works for one value of $x$ (Neal's suggestion is good here), then your answer is correct. – 2012-05-13