Question

Find the interval of convergence for the series. (Enter your answer using interval notation.)

Answer 1

By the ratio test, the series diverges since the limit

$\displaystyle \lim_{n\to\infty} \left| \frac{(n+1)! (4x-1)^{n+1}}{n! (4x-1)^n} \right| = \lim_{n\to\infty} |n+1| |4x-1|$

is not finite.

The series only converges for x = 1/4.