sequences

The sequences (an), (bn), and (cn) are defined by a0 = 1, b0 = 0, c0 = 0, and
an = an-1 + cn-1 / n, bn = bn-1 + an-1 / n, cn = cn-1 + bn-1 / n
for all n>=1.

Prove that:
| an – (n+1)/3 | < 2 / sqrt(3n) for all n>=1

所有跟帖： 

• 回复：sequences -蓝糊涂- ♂ (49 bytes) () 01/14/2010 postreply 06:30:15

• Let me try -innercool- ♀ (766 bytes) () 01/14/2010 postreply 14:02:36

• 回复：Let me try -蓝糊涂- ♂ (40 bytes) () 01/15/2010 postreply 06:14:28

• 回复：回复：Let me try -innercool- ♀ (593 bytes) () 01/15/2010 postreply 08:33:55

• 回复：回复：回复：Let me try -蓝糊涂- ♂ (0 bytes) () 01/15/2010 postreply 08:39:07

• 回复：回复：回复：Let me try -蓝糊涂- ♂ (5 bytes) () 01/15/2010 postreply 08:41:14

• 回复：回复：回复：Let me try -jinjing- ♀ (73 bytes) () 01/15/2010 postreply 11:39:57

• master jinjing不得了。数学顶瓜瓜，提琴也会拉：） -戏雨飞鹰- ♀ (0 bytes) () 01/15/2010 postreply 18:42:08

• 回复：sequences -haha2000- ♂ (277 bytes) () 01/15/2010 postreply 07:18:25

• 回复：回复：sequences -蓝糊涂- ♂ (61 bytes) () 01/15/2010 postreply 08:37:04