问题 填空题
1
1•2
+
1
2•3
+…+
1
n(n+1)
=______.
答案

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

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

=1-

1
n+1
=
n
n+1

故答案为:

n
n+1

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