计算1/x(x+1) +1/x(x+1)(x+2) +1/x(x+2)(x+3) +.+1/x(x+2007)(x+20
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计算1/x(x+1) +1/x(x+1)(x+2) +1/x(x+2)(x+3) +.+1/x(x+2007)(x+2008)并求x=1时,该代数式的值.
![计算1/x(x+1) +1/x(x+1)(x+2) +1/x(x+2)(x+3) +.+1/x(x+2007)(x+20](/uploads/image/z/4715123-59-3.jpg?t=%E8%AE%A1%E7%AE%971%2Fx%28x%2B1%29+%2B1%2Fx%28x%2B1%29%28x%2B2%29+%2B1%2Fx%28x%2B2%29%28x%2B3%29+%2B.%2B1%2Fx%28x%2B2007%29%28x%2B20)
1/x(x+1) +1/x(x+1)(x+2) +1/x(x+2)(x+3) +.+1/x(x+2007)(x+2008)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2007-1/2008)+(1/2008-1/2009)展开括号合并
=1-1/2009
=2008/2009
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2007-1/2008)+(1/2008-1/2009)展开括号合并
=1-1/2009
=2008/2009
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