已知数列an的前n项和Sn=2n^2+n,则lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]的值为

Sn =2n^2+n
Sn-1=2(n-1)^2+n-1
an=Sn -Sn-1
=4n-1
lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]
=lim[1/3*1/7+1/7*1/11+1/11*1/15
=1/4lim[1/3-1/7+1/7-1/11+1/11-1/15
=1/4*1/3
=1/12
选B1/4lim[1/3-1/7+1/7-1/11+1/11-1/15这 步是怎么得出的1/3*1/7=1/21=1/4*4/21=1/4*（1/3-1/7）