so sánh b với 11/21

\(B = \left( {\frac{1}{4} - 1} \right)\left( {\frac{1}{9} - 1} \right)...\left( {\frac{1}{{100}} - 1} \right)\)

\(B = - \frac{3}{4}. - \frac{8}{9}... - \frac{{99}}{{100}}\)

\(B = - \frac{{3.8...99}}{{4.9...100}}\)

\(B = - \frac{{1.3.2.4...9.11}}{{2.2.3.3...10.10}}\)

\(B = - \frac{{\left( {1.2.3...9} \right).\left( {3.4....11} \right)}}{{\left( {2.3...10} \right).\left( {2.3...10} \right)}}\)

\(B = - \frac{{1.11}}{{10.2}} = - \frac{{11}}{{20}} < - \frac{{11}}{{21}}\)

Vậy \(B < - \frac{{11}}{{21}}\)