calculus please solve

Question

Use the ratio test to find the radius of convergence of the power series

1+2!𝑥+4!𝑥^2/(2!)²+6!𝑥^3/(3!)²+8!𝑥⁴ /(4!)²+10!𝑥^57(5!)32+⋯

𝑅=R=  

(If the radius is infinite, enter Inf for R.)

Answer 1

The ratio test will tell you that this series converges for |x|<1/4

Sorry I submitted an incorrect answer at first!

Remember to be careful with (2n)!.