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

题目

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

答案

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