Question8 Mark for Review 40
The radius of convergence of the power series $\sum_{n=0}^{\infty} \frac{n!(n+1)!}{(2 n)!} x^{n}$ is (A) 0
B 1 (C) 2 (D) 4

Studdy Solution
The radius of convergence $R$ is the reciprocal of the limit found in the ratio test. Since the limit is 0, the radius of convergence is infinite.
Therefore, the radius of convergence is $\boxed{4}$.
The correct answer is (D) 4.