Răspuns:
[tex]a=\frac{1}{5*6}+\frac{1}{6*7}+...+\frac{1}{70*71}+\frac{1}{71}=\frac{6-5}{6*5}+\frac{7-6}{6*7}+...+\frac{71-70}{70*71}+\frac{1}{71}=\frac{6}{5*6}-\frac{5}{5*6}+\frac{7}{6*7}-\frac{6}{6*7}+...+\frac{71}{70*71}-\frac{70}{71*70}+\frac{1}{71}=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{70}-\frac{1}{71}+\frac{1}{71}=\frac{1}{5}[/tex]
[tex]\frac{1}{5}<1[/tex]
Explicație pas cu pas:
Am scris 1 ca 6-5, 7-6, 8-7,....71-70. Si am descompus fractia in 2 am pastrat numitorul si am luat cate un numarator pe rand. La final se observa simplificarea.
