Question

若丨ab-2丨+丨b-1丨=0,试求ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+1995）（b+1995)分之1

Answer 1

丨ab-2丨+丨b-1丨=0
丨b-1丨=0
丨ab-2丨=0
b=1
a=2
1/ab+1/（a+1)(b+1)+.......+1/（a+1995)(b+1995)
=1/1*2+1/2*3+1/3*4+...+1/(1996*1997)
=1-1/2+1/2-1/3+1/3-1/4+...+1/1996-1/1997
=1-1/1997
=1996/1997

Answer 2

丨ab-2丨+丨b-1丨=0 ab=2, b=1 ∴a=2,b=1
ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+1995）（b+1995)分之1
=1／2＋1／﹙3×2﹚＋1／﹙4×3﹚＋……＋1／﹙1997×1996﹚
=1－1／2＋1／2－1／3＋1／3－1／4＋……＋1／1996－1／1997
=1－1／1997
=1996／1997

Answer 3

1996/1007