(1-1/15)*(1-1/21)*(1-1/28)*….*(1-1/210)

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1. Đáp án:

    

   Giải thích các bước giải:

   { 1-1/15 } x {  1-1/21 } -x { 1-1/28 } x ….. x { 1 – 1/210 }

    = 14/15x* 20/21 x 27/28 x …… x209/210

    = 28/20 x 40/42 x 54/56 x ……. x 418/420

    = 4×7/5×6 * 5×8/6×7 * 6×9/7×8 * ……. * 19×22/20×21

    = 4x5x6x…..x19/5x6x7x8x…..x20 * 7x8x9x……22/ 6x7x8x…..21

    = 4/20 x 22/6

    = 11/15

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2. $(1-\dfrac{1}{15}) \times (1- \dfrac{1}{21}) \times (1 – \dfrac{1}{28}) \times ….. \times (1 – \dfrac{1}{210}$

   $= \dfrac{14}{15} \times \dfrac{20}{21} \times \dfrac{27}{28} \times ….. \times \dfrac{209}{210}$

   $= \dfrac{28}{30} \times \dfrac{40}{42} \times \dfrac{54}{56} \times …. \times \dfrac{418}{420}$

   $= \dfrac{4\times7}{5\times6} \times \dfrac{5\times8}{6\times7} \times \dfrac{6\times9}{7\times8} \times …. \times \dfrac{19\times22}{20\times21}$

   $= \dfrac{4\times5\times6\times…….\times19}{5\times6\times7\times…..\times20} \times \dfrac{7\times8\times9\times……\times22}{6\times7\times8\times…..\times 21}$

   $= \dfrac{1}{5} \times \dfrac{11}{3}$

   $= \dfrac{11}{15}$

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