Hi

To get the Taylor's series of f(x) around x=0

you need to get

If 1-4x)^{\frac{1}{2}-n}" alt="f^{(n)}(x) = u_n\1-4x)^{\frac{1}{2}-n}" />

you can show that

2n-1)" alt="u_{n+1} = 2\:u_n\2n-1)" />

which leads to

Then

For the last part, you are getting:

But has an infinite limit for x=0