> 数学 >
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
人气:219 ℃ 时间:2020-01-30 09:57:25
解答
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.
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