Chứng minh rằng:

1, Chứng minh rằng:
$$\begin{gathered} a, \frac{1}{2}<\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}<1 \\ b, \frac{7}{12}<\frac{1}{21}+\frac{1}{22}+...+\frac{1}{40}<\frac{5}{6} \end{gathered}$$