1 |
2×4 |
1 |
8 |
1 |
4(1+1) |
1 |
8 |
(2)假设n=k(k≥1.k∈N*)时等式成立,
即
1 |
2×4 |
1 |
4×6 |
1 |
6×8 |
1 |
2k(2k+2) |
k |
4(k+1) |
那么当n=k+1时,
1 |
2×4 |
1 |
4×6 |
1 |
6×8 |
1 |
2k(2k+2) |
1 |
2(k+1)[2(k+1)+2] |
=
k |
4(k+1) |
1 |
4(k+1)(k+2) |
=
k(k+2)+1 |
4(k+1)(k+2) |
=
(k+1)2 |
4(k+1)(k+2) |
=
k+1 |
4[(k+1)+1] |
即n=k+1时等式成立.由(1)、(2)可知,对任意n∈N*等式均成立.