求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值搞错了.若|x-1|+(xy-2)2=0,求求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值
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![求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值搞错了.若|x-1|+(xy-2)2=0,求求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值](/uploads/image/z/2733312-48-2.jpg?t=%E6%B1%821%2Fxy%2B1%2F%28x%2B1%29%28y%2B1%29%2B1%2F%28x%2B2%29%28y%2B2%29%2B%E2%80%A6%2B1%2F%28x%2B2009%29%28y%2B2009%29%2B1%2F%EF%BC%88x%2B2010%EF%BC%89%EF%BC%88y%2B2010%EF%BC%89%E7%9A%84%E5%80%BC%E6%90%9E%E9%94%99%E4%BA%86.%E8%8B%A5%7Cx-1%7C%2B%28xy-2%292%3D0%2C%E6%B1%82%E6%B1%821%2Fxy%2B1%2F%28x%2B1%29%28y%2B1%29%2B1%2F%28x%2B2%29%28y%2B2%29%2B%E2%80%A6%2B1%2F%28x%2B2009%29%28y%2B2009%29%2B1%2F%EF%BC%88x%2B2010%EF%BC%89%EF%BC%88y%2B2010%EF%BC%89%E7%9A%84%E5%80%BC)
求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值搞错了.若|x-1|+(xy-2)2=0,求求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值
求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值
搞错了.若|x-1|+(xy-2)2=0,求
求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值
求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值搞错了.若|x-1|+(xy-2)2=0,求求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2009)(y+2009)+1/(x+2010)(y+2010)的值
如果 |x - 1| + (xy - 2)^2 = 0
那么|x - 1| = 0,xy - 2 = 0
从中解得 x = 1,y = 2
那么
1/xy + 1/(x+1)(y+1) + ··· + 1/(x+2010)(y+2010)
= 1 / (1·2) + 1 / (2·3) + ··· + 1/ (2011·2012)
= 1 - 1/2 + 1/2 - 1/3 +1/3 - ··· +1/2011 - 1/2012
= 1- 1/2012
= 2011 / 2012
做题思路:首先通过题目所给的式子可以求得x和y的值
后面利用1/[n(n+1)] = 1/n - 1/(n+1)这个裂项公式可以求出最后答案