# Math Help - Ratio Test

1. ## Ratio Test

Use the ratio test to prove that

converges,at least for x>0.

2. Originally Posted by matty888
Use the ratio test to prove that

converges,at least for x>0.
$\lim_{n\to\infty}\frac{x\cdot{x^{n}}}{(n+1)n!}\cdo t\frac{n!}{x^n}\Rightarrow\lim_{n\to\infty}\frac{x }{n+1}=0<1$

3. ## Further help plz!

hey thanks for replying to all my questions,could you please explain how you got the first part of this?

4. Originally Posted by matty888
hey thanks for replying to all my questions,could you please explain how you got the first part of this?
Definition of ratio test is if $\lim_{n\to\infty}\frac{a_{n+1}}{a_n}<1$ it converges....so $a_{n+1}=\frac{x^{n+1}}{(n+1)!}=\frac{x\cdot{x^{n}} }{(n+1)n!}$ and divding by a_n is the same as multiplying by its reciporcal which would be $\frac{n!}{x^{n}}$