分式的加减法习题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)

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分式的加减法习题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)
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分式的加减法习题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)
分式的加减法习题
计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)

分式的加减法习题计算1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)+...+1/(a+2006)(a+2007)
1/a(a+1)=1/a-1/(a+1)
所以原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2006)-1/(a+2007)
=1/a-1/(a+2007)
=2007/a(a+2007)