- #1
vbrasic
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Homework Statement
Show that $$\frac{(-1)^nn!}{z^n}$$ is divergent.
Homework Equations
We can use the ratio test, which states that if, $$\lim_{n\to\infty}\bigg|\frac{a_{n+1}}{a_n}\bigg|>1$$ a series is divergent.
The Attempt at a Solution
Applying the ratio test, we find that $$\bigg|\frac{a_{n+1}}{a_n}\bigg|=\frac{n+1}{z}.$$ I'm having trouble showing why the limit of this must be greater than one.