( 1-1/2 ) x ( 1- 1/3 ) x ( 1-1/4 ) x ( 1- 1/5 )x ……….x (1- 1/2003) x (1- 1/2004 )

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1. `( 1-1/2 ) × ( 1- 1/3 ) × ( 1-1/4 ) × ( 1- 1/5 ) × … × (1- 1/2003) × (1- 1/2004 )`

   `= (2/2-1/2)×(3/3-1/3)×(4/4-1/4)×(5/5- 1/5)× … ×(2003/2003-1/2003)×(2004/2004-1/2004 )`

   `= 1/2 × 2/3 × … × 2002/2003 × 2003/2004`

   `= {1 × 2 × … × 2002 × 2003}/{2 × 3 × … × 2002 × 2003 × 2004}`

   `= 1/2004`

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2. `(1-1/2)×(1-1/3)×(1-1/4)×(1-1/5)×…×(1-1/2003)×(1-1/2004)`

   `=1/2×2/3×3/4×4/5×…×2002/2003×2003/2004`

   `={1×2×3×4×…×2002×2003}/{2×3×4×5×…×2003×2004}`

   `=1/2004`

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