计算:(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)

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计算:(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)

计算:(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)
计算:(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)

计算:(1-1/2+1/3-1/4+...+1/2007-1/2008)/(1/1005+1/1006+1/1007+...+1/2008)
000000000000

∵(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)
=(1+1/2+1/3+1/4+1/5-…+1/2007+1/2008)-2×(1/2+1/4+1/6+…+1/2008)
=1+1/2+1/3+1/4+1/5-…+1/2007+1/2008-1-1/2-1/3-1/4-…-1/1004
∴原式=(1/1005+1/1006+…+1/2008)÷(1/1005+1/1006+…+1/2008)
=1