Ta có \(B=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}.....\frac{100}{2}\)
\(B=\frac{51.52.53.....100}{2^{50}}\)
\(B=\frac{1.2.3.4.5.....50.51.52.53.....100}{2^{50}.1.2.3.4.5.....50}\)
\(B=\frac{\left(1.3.5.....99\right).\left(2.4.6.....100\right)}{\left(2.1\right).\left(2.2\right).\left(2.3\right).....\left(2.50\right)}\)
\(B=\frac{\left(1.3.5.....99\right).\left(2.4.6.....100\right)}{2.4.6.....100}\)
\(B=1.3.5.....99< A\)
\(\Rightarrow B< A\)
VậyB<A