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七年级下册数学.长江作业本.暑假作业 例讲11

p15.19已知a,b满足√(a-1) √(b-2)=0，求(1/ab) (1/(a 1)(b 1)) (1/(a 2)(b 2)) (1/(a 3)(b 3)) ...

(1/(a 2018)(b 2018))的值。

解：∵√(a-1) √(b-2)=0

∴a=1,b=2

∴(1/ab)=(1/2)=1-(1/2)

(1/(a 1)(b 1))= (1/(1 1)(2 1))=(1/2)-(1/3)

(1/(a 2)(b 2))= (1/(1 2)(2 2))=(1/3)-(1/4)

(1/(a 3)(b 3))= (1/(1 3)(2 3))=(1/4)-(1/5)

∴(1/ab) (1/(a 1)(b 1)) (1/(a 2)(b 2)) (1/(a 3)(b 3)) ... (1/(a 2018)(b 2018))

=(1-(1/2)) ((1/2)-(1/3)) ((1/3)-(1/4)) ((1/4)-(1/5)) ... ((1/2019)-(1/2020))

=1-(1/2020)

=(2019/2020)