`Answer:`

\(C=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{210}\right)\)

\(=\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{6}{6}-\frac{1}{6}\right)\left(\frac{10}{10}-\frac{1}{10}\right)\left(\frac{15}{15}-\frac{1}{15}\right)...\left(\frac{210}{210}-\frac{1}{210}\right)\)

\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{209}{210}\)

\(=\frac{2.2}{3.2}.\frac{5.2}{6.2}.\frac{9.2}{10.2}...\frac{209.2}{210.2}\)

\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{418}{420}\)

\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{19.22}{20.21}\)

\(=\frac{1.4.2.5.3.6...19.22}{2.3.3.4.4.5...20.21}\)

\(=\frac{\left(1.2.3...19\right)\left(4.5.6...22\right)}{\left(2.3.4...20\right)\left(3.4.5...21\right)}\)

\(=\frac{11}{30}\)

5/3

= 1/3 : 1/5 = 1/3 x 5 = 5/3

5\3

\(B=-1-\frac{1}{3}-\frac{1}{6}-...-\frac{1}{1225}\)

\(=-2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\)

\(=-2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(=-2\left(1-\frac{1}{50}\right)=-2\cdot\frac{49}{50}=-\frac{49}{25}\)

\(B=-1-\frac{1}{3}-\frac{1}{6}-\frac{1}{10}-\frac{1}{15}-...-\frac{1}{1225}\)

\(B=-2\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{49\cdot50}\right)\)

\(B=-2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(B=-2\left(1-\frac{1}{50}\right)\)

\(B=-2\cdot\frac{49}{50}\)

\(B=-\frac{49}{25}\)