[tex]x=\frac{1}{2} \frac{3}{4} \frac{5}{6} \frac{7}{8}...\frac{99}{100} \\\\y=\frac{2}{3} \frac{4}{5} \frac{6}{7} \frac{8}{9}...\frac{100}{101} \\\\x*y=(\frac{1}{2} \frac{3}{4} \frac{5}{6} \frac{7}{8}...\frac{99}{100} )(\frac{2}{3} \frac{4}{5} \frac{6}{7} \frac{8}{9}...\frac{100}{101})\\[/tex]
Se intercaleaza termenii
[tex]x*y=\frac{1}{2}\frac{2}{3}\frac{3}{4}\frac{4}{5}...\frac{98}{99}\frac{99}{100}\frac{100}{101}[/tex]
Se se simplifica 2cu2,3cu3,4cu4,...,100cu100
Ramane:
[tex]x*y=\frac{1}{101}[/tex]
