Ta có: \(B=\frac{1}{112}-\frac{1}{84}-\frac{1}{60}-\frac{1}{40}-\frac{1}{24}-\frac{1}{12}-\frac{1}{4}\)
\(\Rightarrow2B=\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(\Rightarrow2B=\frac{1}{56}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\left(1-\frac{1}{7}\right)\)
\(\Rightarrow2B=\frac{1}{56}-\frac{6}{7}\)
\(\Rightarrow2B=-\frac{47}{56}\)
\(\Rightarrow B=-\frac{47}{112}\)
Hok tốt nha^^
