1 |
3 |
1 |
4 |
1 |
5 |
1 |
6 |
57 |
60 |
50 |
60 |
5 |
6 |
(2)假设n=k(k≥2,k∈N*)时命题成立,即
1 |
k+1 |
1 |
k+2 |
1 |
3k |
5 |
6 |
则当n=k+1时,左边=
1 |
(k+1)+1 |
1 |
(k+1)+2 |
1 |
3k |
1 |
3k+1 |
1 |
3k+2 |
1 |
3(k+1) |
=
1 |
k+1 |
1 |
k+2 |
1 |
3k |
1 |
3k+1 |
1 |
3k+2 |
1 |
3k+3 |
1 |
k+1 |
>
5 |
6 |
1 |
3k+3 |
1 |
k+1 |
5 |
6 |
所以当n=k+1时不等式也成立.
综上由(1)(2)可知:原不等式对任意n≥2(n∈N*)都成立.