tính a (1-1/3)(1-1/6)(1-1/10)(1-1/15). … .(1-1/780) x a = 1

0 bình luận về “tính a (1-1/3)(1-1/6)(1-1/10)(1-1/15). … .(1-1/780) x a = 1”

1. `( 1 – 1/3 ) × ( 1 – 1/6 ) × ( 1 – 1/10 ) × ( 1 – 1/15 ) × … × ( 1 – 1/780 ) × a = 1`

   `2/3 × 5/6 × 9/10 × 14/15 × … × 779/780 × a = 1`

   `4/6 × 10/12 × 18/20 × 28/30 × … × 1558/1560 × a = 1`

   `{4 × 1}/{2 × 3} × {5 × 2}/{3 × 4} × {6 × 3}/{4 × 5} × {7 × 4}/{5 × 6} × …. × {41 × 38}/{39 × 40} × a = 1`

   `{1 × 41}/{3 × 39} × a = 1`

   `41/117 × a = 1`

                   `a = 1 : 41/117`

                   `a = 117/41`

   `#dtkc`

    

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2. `(1-1/3)×(1-1/6)×(1-1/10)×(1-1/15)×….×(1-1/780)×a=1`
   `=>2/3×5/6×9/10×14/15×…×779/780×a=1`
   `=>4/6×10/12×18/20×28/30×…×1558/1560×a=1`
   `=>(1×4)/(2×3)×(2×5)/(3×4)×(3×6)/(4×5)×….×(38×41)/(39×40)×a=1`
   `=>((1×2×…×38)×(4×5×6×…×41))/((2×3×4×…×39)×(3×4×5×…×40))×a=1`
   `=>(1×41)/(39×3)=41/117×a=1`
   `=>a=1:41/117`
   `=>a=117/41`

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