Question

( 1- 1/6 ) x ( 1- 1/9 ) x ( 1- 1/16 ) x ........x ( 1- 1/100 ) x ( 1-1/121)

Answer 1

      \(\left(1-\frac{1}{6}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{100}\right).\left(1-\frac{1}{121}\right)\)

\(=\frac{5}{6}.\frac{8}{9}.\frac{15}{16}.....\frac{99}{100}.\frac{120}{121}\)

\(=\frac{5}{6}.\left(\frac{2.4}{3^3}.\frac{3.5}{4^2}.....\frac{9.11}{10^2}.\frac{10.12}{11^2}\right)\)

\(=\frac{5}{6}.\left[\left(\frac{2}{3}.\frac{3}{4}.....\frac{9}{10}.\frac{10}{11}\right).\left(\frac{4}{3}.\frac{5}{4}....\frac{11}{10}.\frac{12}{11}\right)\right]\)

\(=\frac{5}{6}.\frac{2}{11}.\frac{12}{3}\)

\(=\frac{5}{33}.4\)

\(=\frac{20}{33}\)

Answer 2

Thanks!