$$\sum_{n=1}^\infty (-1)^n\frac{n}{10^n}$$
I am trying to show that $|a_{n+1}|$ is less than or equal to $|a_n|$
So I have $\frac{n+1}{10^{n+1}}$ less than or equal to $\frac{n}{10^n}$.
And then that $\lim_{n\to\infty} a_n = 0$
Both are supposedly true and makes the series convergent but when I do it I get not true for both conditions and then divergent for the series, which is wrong.