Binomial Series -- from Wolfram MathWorld
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
The Maclaurin series is a Taylor series around x=0:
where 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 and take the derivative to make sure it matches .
In some cases, you can just take the first few derivatives and write your answer like:
with the correct values substituted, of course.
Post again in this thread if you're still having trouble.