1\(19*21)+1\(21*23)+1\(23*25)+...+1\(97*99)简便,

1\(19*21)+1\(21*23)+1\(23*25)+...+1\(97*99)简便,
1\(19*21)+1\(21*23)+1\(23*25)+...+1\(97*99)
简便,

1\(19*21)+1\(21*23)+1\(23*25)+...+1\(97*99)简便,
1\(19*21)+1\(21*23)+1\(23*25)+...+1\(97*99)
=1/2[(1/19-1/21)+(1/21-1/23)+...+(1/97-1/99)]
=1/2(1/19-1/99)
=40/1881

1\(19*21)+1\(21*23)+1\(23*25)+...+1\(97*99)
=1/2(1/19-1/21)+1/2(1/21-1/23)+...+1/2(1/97-1/99)
=1/2(1/19-1/21+1/21-1/23+...+1/97-1/99)
=1/2(1/19-1/99)
=40/19*99

原式=1/2(1/19-1/21+...-1/99)=1/2(1/19-1/99)我手机上的没草稿纸 麻烦你自己通下分嘛