Bài giải

Ta có :

$\frac{1}{1}-\frac{1}{4}=\,\frac{3}{1\times 4}$

$\frac{1}{4}-\frac{1}{7}=\frac{3}{4\times 7}$

......

=> $\frac{1}{1\times 4}+\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$

  = $\frac{1}{3}\times \left( \frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16} \right)$

  = $\frac{1}{3}\times \left( 1-\frac{1}{16} \right)=\frac{1}{3}\times \frac{15}{16}=\frac{15}{48}=\frac{5}{16}$

Đáp số : $\frac{5}{16}$