\(5B=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{496.501}\)
\(5B=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}+...+\frac{501-496}{496.501}\)
\(5B=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{496}-\frac{1}{501}\)
\(5B=1-\frac{1}{501}=\frac{500}{501}\Rightarrow B=\frac{100}{501}\)