# Thread: help with ratio test.

1. ## help with ratio test.

heres the test: http://img165.imageshack.us/img165/8305/46745116xr3.png

i'm having lots of trouble with the math for problems like these.

the confusion is right when we multiply by the reciprocal of the original equation.

what happens to the n!/|x|^n ? how does that cancel everything to make it the original problem without any n exponets.

can someone show what is going on for this step, its not exactly the calculus i'm asking about, its just the math in this step.

thanks.

2. $\displaystyle \lim ~ \frac{|x|^{n+1}}{(n+1)!}\cdot \frac{n!}{|x|^n} = \frac{|x|}{n+1} = 0$. Thus, the radius of convergence is $\displaystyle \infty$.