对于任意i≥1i\ge1i≥1，有：
1ai+3ai+2−ai+2ai+1−1ai+2ai+1−ai+1ai=13i+1{\frac{1}{\frac{a_{i+3}}{a_{i+2}} - \frac{a_{i+2}}{a_{i+1}}}} - {\frac{1}{\frac{a_{i+2}}{a_{i+1}} - \frac{a_{i+1}}{a_{i}}}} = \frac{1}{3}i + 1ai+2ai+3−ai+1ai+21−ai+1ai+2−aiai+11=31i+1
1 2 5 14 42 2 2.5
