如果|AB-2|+(B-1)²=0,求1/AB+1/(A+1)(B+1)+.+1/(A+2008)(B+2008)的值
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![如果|AB-2|+(B-1)²=0,求1/AB+1/(A+1)(B+1)+.+1/(A+2008)(B+2008)的值](/uploads/image/z/15209661-21-1.jpg?t=%E5%A6%82%E6%9E%9C%7CAB-2%7C%2B%EF%BC%88B-1%29%26sup2%3B%3D0%2C%E6%B1%821%2FAB%2B1%2F%28A%2B1%29%28B%2B1%29%2B.%2B1%2F%28A%2B2008%29%28B%2B2008%29%E7%9A%84%E5%80%BC)
如果|AB-2|+(B-1)²=0,求1/AB+1/(A+1)(B+1)+.+1/(A+2008)(B+2008)的值
如果|AB-2|+(B-1)²=0,求1/AB+1/(A+1)(B+1)+.+1/(A+2008)(B+2008)
的值
如果|AB-2|+(B-1)²=0,求1/AB+1/(A+1)(B+1)+.+1/(A+2008)(B+2008)的值
从第一部分可以看出b=1,a=2
所以该题就是1/(1*2)+1/(2*3)+……+1/(2009*2010)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=1009/2010
153463
1/(1*2)+1/(2*3)+……+1/(2009*2010)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=1009/2010