$$
\begin{array}{l}
\text { 1. If } \frac{x}{x+1}+\frac{2 x}{(x+1)(2 x+1)}+ \\
\frac{3 x}{(x+1)(2 x+1)(3 x+1)}>1,
\end{array}
$$

then the range of real number $x$ is
$$
\text { II. 1. } x1 .
\end{array}
$$

Therefore $(x+1)(2 x+1)(3 x+1)<0$
$$
\begin{array}{l}
\Rightarrow(x+1)\left(x+\frac{1}{2}\right)\left(x+\frac{1}{3}\right)<0 \\
\Rightarrow x<-1 \text { or }-\frac{1}{2}<x<-\frac{1}{3} .
\end{array}
$$