1/1×2+1/2×3+1/3×4...+1/2006×2007=?

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1/1×2+1/2×3+1/3×4...+1/2006×2007=?
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1/1×2+1/2×3+1/3×4...+1/2006×2007=?
1/1×2+1/2×3+1/3×4...+1/2006×2007=?

1/1×2+1/2×3+1/3×4...+1/2006×2007=?
1/1×2 + 1/2×3 + 1/3×4 + ...+ 1/2006×2007
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/2006 - 1/2007
= 1 - 1/2007
= 2006/2007

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2006-1/2007)
=1-1/2+1/2-1/3+1/3-1/4+…+1/2006-1/2007
=1-1/2007
=2006/2007