Lời giải:
Ta có:
$S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{n.(n+3)}$
$S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}$
$=>S=1-\frac{1}{n+3}$
$=>S=\frac{n+3-1}{n+3}$
$=>S=\frac{n+2}{n+3}$
Mà:$ n+2 < n+3 (n∈N*)$
<Tử nhỏ mẫu>
=>$S<1$