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