limn→∞[1/1•4+1/4•7+1/7•10+…+1/(3n−2)(3n+1)]=_．
问题描述：
[lim n→∞
+1 1•4
+1 4•7
+…+1 7•10
]=______． 1 (3n−2)(3n+1)
答
[lim n→∞
+1 1•4
+1 4•7
+…+1 7•10
]1 (3n−2)(3n+1)
=
lim n→∞
[(1−1 3
)+(1 4
−1 4
)+…+(1 7
−1 3n−2
)1 3n+1
=
lim n→∞
(1−1 3
)1 3n+1
=
lim n→∞
•1 3
=3n 3n+1
．1 3
故答案为
．1 3