问题 选择题
f(n)=
1
n+1
+
1
n+2
+
1
n+3
+…+
1
3n
(n∈N*)
,则f(n+1)-f(n)=(  )
A.
1
3n+1
B.
1
3n+2
C.
1
3n+1
+
1
3n+2
-
2
3n+3
D.
1
3n+1
+
1
3n+2
答案

根据题中所给式子,得f(n+1)-f(n)

=

1
(n+1)+1
+
1
(n+1)+2
+
1
(n+1)+3
+…+
1
3(n+1)
-(
1
n+1
+
1
n+2
+
1
n+3
+…+
1
3n

=

1
3n+1
+
1
3n+2
+
1
3n+3
-
1
n+1

=

1
3n+1
+
1
3n+2
-
2
3n+3

故选C.

单项选择题 A1/A2型题
单项选择题