计算:1/6+1/12+1/20+1/30……+1/2009*2010 简便计算

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计算:1/6+1/12+1/20+1/30……+1/2009*2010 简便计算
计算:1/6+1/12+1/20+1/30……+1/2009*2010 简便计算

计算:1/6+1/12+1/20+1/30……+1/2009*2010 简便计算
6拆成2X3,1/6=1/2-1/3
12拆成3X4,1/12=1/3-1/4
20拆成4X5,1/20=1/4-1/5
以此内推
所以原式
=1/2-1/3+1/3-1/4...+1/2009-1/2010
=1/2-1/2010
=1004/2010
=502/1005

发言人幸苦im

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+.........+1/2009-1/2010
=1/2-1/2010
=1005/2010-1/2010
=1004/2010
=502/1005

=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/2010
=1/2-1/2010
=502/1005

“裂项求和”,可得
1/6+1/12+1/20+1/30……+1/(2009x2010 )
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/2010
=1/2-1/2010
= 502/1005