$\frac{3}{4}$x$\frac{8}{9}$x$\frac{15}{16}$x….x$\frac{899}{900}$

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1. `3/4 . 8/9 . 15/16 … 899/900`

   `=1.3/2^2 . 2.4/3^2 . 3.5/4^2 … 29.31/30^2`

   `=1.3/2.2 . 2.4/3.3 . 3.5/4.4 … 29.31/30.30`

   `={1.3.2.4.3.5…29.31}/{2.2.3.3.4.4…30.30}`

   `={1.31}/{2.30}`

   `=31/60`

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2. =1×3/2×2  ×  2×4/3×3  ×  3×5/4×4 × …..  × 29×31/30×30

   =1×2×3  ×… × 29/2×3×4…×30   ×    3×4×5…×31/2×3×4…×30

   = 1/30. 31/2=31/60

    

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