So sánh \(\frac{{2005}}{{2006}}\) và \(\frac{{2006}}{{2007}}\).

Ta xét: 1 – \(\frac{{2005}}{{2006}} = \frac{1}{{2006}}\)

1 – \(\frac{{2006}}{{2007}} = \frac{1}{{2007}}\)

Ta thấy: \(\frac{1}{{2006}}\)> \(\frac{1}{{2007}}\)nên : 1 – \(\frac{{2005}}{{2006}}\)> 1 –\(\frac{{2006}}{{2007}}\)

Suy ra: \(\frac{{2005}}{{2006}}\) < \(\frac{{2006}}{{2007}}\).