1. ## Mclaurin Series.

The question is: . Find the Maclaurin series of f (x) = (1 + x^2)^(3/2)
Not sure where to start I think you might have to use the formula (1+a)^k.. but still don't know what to do

2. Binomial Series -- from Wolfram MathWorld

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. The Maclaurin series is a Taylor series around x=0:

$\displaystyle f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n$

where $\displaystyle f^{(n)}(0)$ is the n-th derivative of f(x) evaluated at x=0. To get an expression for the n-th derivative, it usually works to do the first 3 or 4 and you start to see a pattern. Then you can write $\displaystyle f^{(n)}(x)$ and take the derivative to make sure it matches $\displaystyle f^{(n+1)}(x)$.

In some cases, you can just take the first few derivatives and write your answer like:

$\displaystyle f(x)=f(0)+f'(0)x+\frac{f''(0)}{2}x^2+\frac{f'''(0) }{6}x^3+...$

with the correct values substituted, of course.

Post again in this thread if you're still having trouble.