计算1/1*2+1/2*3+1/3*4+...+1/2009*2010的值

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计算1/1*2+1/2*3+1/3*4+...+1/2009*2010的值

计算1/1*2+1/2*3+1/3*4+...+1/2009*2010的值
计算1/1*2+1/2*3+1/3*4+...+1/2009*2010的值

计算1/1*2+1/2*3+1/3*4+...+1/2009*2010的值
1/1*2+1/2*3+1/3*4+...+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010

1/1*2+1/2*3+1/3*4+...+1/2009*2010
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010

1/1*2+1/2*3+1/3*4+...+1/2009*2010
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2009-1/2010)
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010

1/1*2+1/2*3+1/3*4+...+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010