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x=2 ,y=1,计算xy分之一+(x+1)(y+1)分之一+....+(x+2010)(y+2010)的值
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解:
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2010)(y+2010)
=1/(1*2)+1/(2*3)+1/(3*4)+......+1/(2011*2012)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/20011-1/2012
=1/1-1/2012
=2011/2012
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+…+1/(x+2010)(y+2010)
=1/(1*2)+1/(2*3)+1/(3*4)+......+1/(2011*2012)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/20011-1/2012
=1/1-1/2012
=2011/2012
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