计算:(1/2+1/3+…+1/2002)(1+1/2+1/3+…+1/2001)−(1+1/2+…+1/2002)(1/2+1/3+…+1/2001)
问题描述:
计算:(
+1 2
+…+1 3
)(1+1 2002
+1 2
+…+1 3
)−(1+1 2001
+…+1 2
)(1 2002
+1 2
+…+1 3
) 1 2001
答
假设:a=1+
+1 2
+…1 3
,b=1 2001
+1 2
+…+1 3
,1 2001
即a-b=1,
∴原式=(b+
)a-(a+1 2002
)b,1 2002
=ab+a×
-ab-b×1 2002
,1 2002
=(a-b)×
1 2002
又∵a-b=1
∴原式=
1 2002