1/1×2+1/2×3+1/3×4+……+1/2002×2003.

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1/1×2+1/2×3+1/3×4+……+1/2002×2003.

1/1×2+1/2×3+1/3×4+……+1/2002×2003.
1/1×2+1/2×3+1/3×4+……+1/2002×2003.
 

1/1×2+1/2×3+1/3×4+……+1/2002×2003.
1/n(n+1) = 1/n - 1/(n+1)
1/1×2+1/2×3+1/3×4...+1/2002×2003
= (1/1 - 1/2) +(1/2 - 1/3) + (1/3 - 1/4) +...+ (1/2002 -1/2003 )
= 1 - 1/2003 = 2002/2003