\(B=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right)...\left(1-\frac{1}{10000}\right)\)
\(=\left(\frac{4}{4}-\frac{1}{4}\right).\left(\frac{9}{9}-\frac{1}{9}\right)...\left(\frac{10000}{10000}-\frac{1}{10000}\right)\)
\(=\frac{3}{4}.\frac{8}{9}...\frac{9999}{10000}=\frac{3}{2.2}.\frac{2.4}{3.3}...\frac{99.101}{100.100}\)
\(=\frac{101}{100}\)
\(D=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)
\(=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)
\(=5.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5.\left(\frac{1}{1}-\frac{1}{31}\right)=5.\left(\frac{31}{31}-\frac{1}{31}\right)=5.\frac{30}{31}=\frac{150}{31}\)
