Tính ​\(\begin{aligned} &\mathrm{B}=\frac{1}{1.6}+\frac{1}{6.11}+\cdots+\frac{1}{496.501} \end{aligned}\)

* Hướng dẫn giải

Ta có:

  \(\begin{aligned} &\mathrm{B}=\frac{1}{1.6}+\frac{1}{6.11}+\cdots+\frac{1}{496.501} \\ &\mathrm{~B}=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\cdots+\frac{1}{496}-\frac{1}{501}\right)\\ &\mathrm{B}=\frac{1}{5}\left(1-\frac{1}{501}\right)=\frac{100}{501} \end{aligned}\)