[tex]1\frac{1}{2}*1\frac{1}{3}*..*1\frac{1}{100}=\\ \\=\frac{2*1+1}{2}*\frac{3*1+1}{3}*..\frac{100*1+1}{100}\\ \\=\frac{3}{2}*\frac{4}{3}*..*\frac{101}{100}\\ \\simplificam\\\\=\frac{101}{2}\\ \\=50\frac{1}{2}[/tex]
