（1/1+2）+（1/1+2+3）+（1/1+2+3+4）+.......+(1/1+2+....+2005)
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1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.......+1/(1+2+....+2005)
= 2/(2×3)+2/(3×4)+2/(4×5)+.......+2/(2005×2006)
= 2[1/(2×3)+1/(3×4)+1/(4×5)+.......+1/(2005×2006)]
= 2[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.......+(1/2005-1/2006)]
= 2(1/2-1/2006)
= 1-1/1003
= 1002/1003
= 2/(2×3)+2/(3×4)+2/(4×5)+.......+2/(2005×2006)
= 2[1/(2×3)+1/(3×4)+1/(4×5)+.......+1/(2005×2006)]
= 2[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.......+(1/2005-1/2006)]
= 2(1/2-1/2006)
= 1-1/1003
= 1002/1003
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