Có: \(\frac{1}{2^{2}} < \frac{1}{1.2} ; \frac{1}{3^{2}} < \frac{1}{2.3} ; . . . ; \frac{1}{8^{2}} < \frac{1}{7.8}\)
\(\Rightarrow B < \frac{1}{1.2} + \frac{1}{2.3} + . . . + \frac{1}{7.8}\)
\(\Rightarrow B < 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + . . . + \frac{1}{7} - \frac{1}{8}\)
\(\Rightarrow B < 1 - \frac{1}{8} < 1\)
\(\Rightarrow B < 1\) \(\Rightarrow đ p c m\)