问题 解答题
计算
1
2
1
+
2
+
1
3
2
+2
3
+
1
4
3
+3
4
+…+
1
2004
2003
+2003
2004
答案

1
(n+1)
n
+n
n+1
=
(n+1)
n
-n
n+1
(n+1)2n-n2(n+1)

=

(n+1)
n
-n
n+1
n(n+1)

=

1
n
-
1
n+1

∴原式=1-

1
2
+
1
2
-
1
3
+
1
3
-
1
4
+…+
1
2003
-
1
2004

=1-

1
2004

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