问题
解答题
若a，b为实数，且|a-1|+
|
答案
∵a，b为实数，当ab≥2，a≥1时，
|a-1|与
均为非负数，ab-2
由非负数性质：
∴a=1，b=2a-1=0 ab-2=0
∴
+1 ab
+1 (a+1)(b+1)
+…+1 (a+2)(b+2) 1 (a+1999)(b+1999)
=
+1 1×2
+1 2×3
+…+1 3×4 1 2000×2001
=1-
+1 2
-1 2
+1 3
-1 3
+…+1 4
-1 2000 1 2001
=1-1 2001
=
．2000 2001