(1/2+1/3+…+1/2005)(1+1/2+1/3+…+1/2004)-(1+1/2+1/3+…+1/2005)(1/2+1/3+…+1/2004).

问题描述:

1
2
+
1
3
+…+
1
2005
)(1+
1
2
+
1
3
+…+
1
2004
)-(1+
1
2
+
1
3
+…+
1
2005
)(
1
2
+
1
3
+…+
1
2004
).

设a=

1
2
+
1
3
+…+
1
2005
,b=
1
2
+
1
3
+…+
1
2004
,则原式=a(1+b)-b(1+a)=a+ab-b-ab=a-b=
1
2005