如果lab-2l+(b-1)的2次幂=0,试求：1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+999)(b+999)的值

如果lab-2l+(b-1)的2次幂=0,试求：1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+999)(b+999)的值
如果lab-2l+(b-1)的2次幂=0,试求：1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+999)(b+999)的值

如果lab-2l+(b-1)的2次幂=0,试求：1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+999)(b+999)的值
∵lab-2l+(b-1)²=0
又∵lab-2l≥0,(b-1)²≥0
要使两个非负数之和为0,必须使得两个数都为0
即lab-2l=0,(b-1)²=0
解得：a=2,b=1
则原式可化为：
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(1000*1001)
=1-1/2+1/2-1/3+1/3-1/4+……+1/1000-1/1001
=1-1/1001
=1000/1001

您好：

lab-2l+(b-1)的2次幂=0
b=1
ab=2
a=2/b=2

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+999)(b+999)
=1/1x2+1/2x3+1/3x4+...+1/1000x1001
=1-1/2+1/2-1/3+1/3-1/4+...+1/1000...

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您好：

lab-2l+(b-1)的2次幂=0
b=1
ab=2
a=2/b=2

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+999)(b+999)
=1/1x2+1/2x3+1/3x4+...+1/1000x1001
=1-1/2+1/2-1/3+1/3-1/4+...+1/1000-1/1001
=1-1/1001
=1000/1001

不明白，可以追问
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