数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?

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数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
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数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?

数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)...+(-1/2007+1/2007)-1/2008
=1-1/2008
=2007/2008

去括号,消项就可以了!

括号展开就一目了然了
=1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)...+(-1/2007+1/2007)-1/2008
=1-1/2008
=2007/2008