1/2*4+1/4*6+1/6*8...+1/2n(2n+2)=1001/4008 最好有解析

列项求和1/[2n*(2n+2)]=1/2*[1/(2n)-1/(2n+2)]原式化为：1/2*[1/2-1/4+1/4-1/6+1/6-1/8+.+1/(2n)-1/(2n+2)]=1001/40081/2-1/(2n+2)=1001/4008*21/2-1/(2n+2)=1001/20041/(2n+2)=1/2-1001/20041/(2n+2)=1/20042n+2=20...