Bài giải:

$100+\frac{1}{10\text{x}11}+\frac{1}{11\text{x}12}+\frac{1}{12\text{x}13}+\frac{1}{13\text{x}14}+\frac{1}{14\text{x}15}$

$=100+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}$

$\begin{align}& =100+\frac{1}{10}-\frac{1}{15} \\& =\frac{3000}{30}+\frac{3}{30}-\frac{2}{30} \\& =\frac{3001}{30} \\\end{align}$