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
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![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](/uploads/image/z/5281154-26-4.jpg?t=%E5%A6%82%E6%9E%9Clab-2l%2B%28b-1%29%E7%9A%842%E6%AC%A1%E5%B9%82%3D0%2C%E8%AF%95%E6%B1%82%EF%BC%9A1%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B...1%2F%28a%2B999%29%28b%2B999%29%E7%9A%84%E5%80%BC)
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
如有帮助,记得采纳,谢谢
祝学习进步!
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