计算：4/ (x+1)(x+3)+4/(x+3)(x+5)+…..+4/(x+2n-1)(x+2n+1)的值?能不能说详细一点哟——fish俊

=2{[1/(x-1)-1/(x-3)]+[1/(x-3)-1/(x-5)]+……+[1/(x+2n-1)-1/(x+2n+1)]}
=2[1/(x-1)-1/(x+2n+1)]
=4(n-1)/[(x-1)(x+2n+1)]

4/ (x+1)(x+3）=2/(x+1) -2/(x+3)
4/ (x+1)(x+3)+4/(x+3)(x+5)+…..+4/(x+2n-1)(x+2n+1)
=2/(x+1) -2/(x+2n+1)