B = (1 + 1/2)(1 + 1/3)(1 + 1/4) ...(1 + 1/100)
= \(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{101}{100}\)
= \(\frac{3.4.5....101}{2.3.4...100}=\frac{101}{2}\)
C = \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{1000}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{999}{1000}\)
\(=\frac{1.2.3...999}{2.3.4....1000}=\frac{1}{1000}\)