急需解决数列问题，谢谢

蛇Sn=1/2+1/6+1/12+....+1/n(n+1),且Sn*S(n+1)=3/4,则 n的值为A 9 B 8 C 7 D 6

热心网友

因为Sn=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+....去括号得Sn=1-1/(n+1)=n/(n+1)同理 S(n+1)=(n+1)/(n+2)又因Sn*S(n+1)=3/4也就是n/(n+2)=3/4n=6D6是对的,

热心网友

楼上两位,可能因求速度未能细说,我来求数列之和:Sn = 1/2+1/6+1/12+....+1/n(n+1) = (1/1-1/2)+(1/2-1/3)+(1/3-1/4)+....(1/n-1/(n+1))=1 -1/(n+1) = n/(n+1);以下略...

热心网友

选D：6Sn = 1/2+1/6+1/12+....+1/n(n+1) = 1 -1/(n+1) = n/(n+1)S(n+1) = (n+1)/(n+2)Sn*S(n+1) = 3/4 = [n/(n+1)]*[(n+1)/(n+2)]== n = 6

热心网友

d 6,,,,,,,,用裂项法，相消！！！