Ta có: \(B=\left(\frac14-1\right)\left(\frac19-1\right)\cdot\ldots\cdot\left(\frac{1}{100}-1\right)\)
\(=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\cdot\ldots\cdot\left(\frac{1}{10^2}-1\right)\)
\(=-\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdot\ldots\cdot\left(1-\frac{1}{10^2}\right)\)
\(=-\left(1-\frac12\right)\left(1-\frac13\right)\cdot\ldots\cdot\left(1-\frac{1}{10}\right)\left(1+\frac12\right)\left(1+\frac13\right)\cdot\ldots\cdot\left(1+\frac{1}{10}\right)\)
\(=-\frac12\cdot\frac23\cdot\ldots\cdot\frac{9}{10}\cdot\frac32\cdot\frac43\cdot\ldots\cdot\frac{11}{10}=-\frac{1}{10}\cdot\frac{11}{2}=-\frac{11}{20}\)
Ta có: 20<21
=>\(\frac{11}{20}>\frac{11}{21}\)
=>\(-\frac{11}{20}<-\frac{11}{21}\)
=>\(B<-\frac{11}{21}\)
