Let f be a function that is known to be analytic in a neighbourhood of the origin in the complex plane. Furthermore it is known that for n ∈ \(\mathbb{N}\),
\(f^{(n)}(0)= (n-1)!(n+1) (\frac{n+1}{n})^{(n+1)(n-1)}\)
Find the radius of the largest circle with centre at the origin inside which the Taylor series of f defines a analytic function.
1
e
2
1/e
3
e2
4
1
5
Question Not Attempted