$將1+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}用A表示,$
$將 \frac{1}{3}+\frac{1}{4}+\frac{1}{5}用B表示。\ $
$原式就可以轉(zhuǎn)換成A×(B+\frac{1}{6})-(A+\frac{1}{6})×B$
$=AB+\frac{1}{6}A-AB-\frac{1}{6}B$
$=\frac{1}{6}\ \mathrm {A}-\frac{1}{6}\ \mathrm {B}$
$=\frac{1}{6}(A-B),$
$因為 A-B$
$= (1+\frac{1}{3}+\frac{1}{4}+\frac{1}{5})-(\frac{1}{3}+\frac{1}{4}+\frac{1}{5})=1,$
$所以\frac{1}{6}(A-B)=\frac{1}{6}×1=\frac{1}{6} 。$