求教大家,这道题有没有什么简便方法呢?

2025-05-10 07:59:52
推荐回答(1个)
回答1:

an = 1/[(2n-1)(2n+1)]
= (1/2)[(2n-1) -1/(2n+1) ]
Sn = a1+a2+...+an
= (1/2)[1 -1/(2n+1) ]
= n/(2n+1)
1/(1x3)+1/(3x5)+...+1/(23x25)
=S12
=12/25
25x[1/(1x3)+1/(3x5)+...+1/(23x25)]
=25x12/25
=12