公式（sum ∑ from k=1 to n）f<sub>k</sub>=f<sub>n+2</sub>-f<sub>2</sub>,（sum ∑ from k=1 to n）f<sub>2k-1</sub>=f<sub>2n</sub>-（f<sub>2</sub>-f...公式（sum ∑ from k=1 to n）f<sub>k</sub>=f<sub>n+2</sub>-f<sub>2</sub>,（sum ∑ from k=1 to n）f<sub>2k-1</sub>=f<sub>2n</sub>-（f<sub>2</sub>-f<sub>1</sub>）（sum ∑ from k=1 to n）f<sub>2k</sub>=f<sub>2n+1</sub>-f<sub>1</sub>,（sum ∑ from k=1 to n）f<sub>k</sub><sup>2</sup>=f<sub>n</sub>f<sub>n+1</sub>（sum ∑ from k=1 to n）f<sub>k</sub>f<sub>k+1</sub>=1/2(f<sub>n+2</sub><sup>2</sup>-f<sub>n</sub>f<sub>n+1</sub>- 中,我们把前三个关于任意的裴波那契序列公式(即 f<sub>n</sub>=f<sub>n-1</sub>+f<sub>u-2</sub>,f<sub>1</sub>=a,f<sub>2</sub>=b)推广到二阶线性递推序列(即 f<sub>n</sub>=pf<sub>n-1</sub>+qf<sub>n-2</sub>,f<sub>1</sub>=a,f<sub>2</sub>=b,p,q,a,b 均为实数);把后两个公式推广到任意的裴波那契序列中去.展开更多
文摘公式（sum ∑ from k=1 to n）f<sub>k</sub>=f<sub>n+2</sub>-f<sub>2</sub>,（sum ∑ from k=1 to n）f<sub>2k-1</sub>=f<sub>2n</sub>-（f<sub>2</sub>-f<sub>1</sub>）（sum ∑ from k=1 to n）f<sub>2k</sub>=f<sub>2n+1</sub>-f<sub>1</sub>,（sum ∑ from k=1 to n）f<sub>k</sub><sup>2</sup>=f<sub>n</sub>f<sub>n+1</sub>（sum ∑ from k=1 to n）f<sub>k</sub>f<sub>k+1</sub>=1/2(f<sub>n+2</sub><sup>2</sup>-f<sub>n</sub>f<sub>n+1</sub>- 中,我们把前三个关于任意的裴波那契序列公式(即 f<sub>n</sub>=f<sub>n-1</sub>+f<sub>u-2</sub>,f<sub>1</sub>=a,f<sub>2</sub>=b)推广到二阶线性递推序列(即 f<sub>n</sub>=pf<sub>n-1</sub>+qf<sub>n-2</sub>,f<sub>1</sub>=a,f<sub>2</sub>=b,p,q,a,b 均为实数);把后两个公式推广到任意的裴波那契序列中去.
