1/2*4+1/4*6+1/6*8...+1/20 - 知识问答

1/2*4+1/4*6+1/6*8...+1/2009*2010

1个回答

是不是把2008敲成2009了,按2008计算
1/2*4+1/4*6+1/6*8...+1/2008*2010
=1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+...+1/2(1/2008-1/2010)
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010)
=1/2(1/2-1/2010)
=1/2(505-1)/2010
=252/2010
=42/335

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