4.Tính nhanh (phân số) : A= 1/5.6 + 1/6.7 + 1/7.8 + ………. + 1/24.25 B= 2/3.5 + 3/5.8 + 11/8.19 + 13/19.32 + 25/32.57 + 30/57.87 5. Cho A =1

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1. Đáp án:

    A = $\dfrac{1}{5.6}$ + $\dfrac{1}{6.7}$ + $\dfrac{1}{7.8}$ + …. + $\dfrac{1}{24.25}$

   = $\dfrac{1}{5}$ -$\dfrac{1}{6}$ + $\dfrac{1}{6}$ -$\dfrac{1}{7}$ + $\dfrac{1}{7}$ – $\dfrac{1}{8}$ +…+ $\dfrac{1}{24}$ – $\dfrac{1}{25}$

    = $\dfrac{1}{5}$ – $\dfrac{1}{25}$

    = $\dfrac{5}{25}$ – $\dfrac{1}{25}$

    = $\dfrac{4}{25}$

   B = $\dfrac{2}{3.5}$ + $\dfrac{3}{5.8}$ + $\dfrac{11}{8.9}$ + $\dfrac{13}{19.32}$ + $\dfrac{25}{32.57}$ + $\dfrac{30}{57.87}$

    = $\dfrac{1}{3}$ – $\dfrac{1}{5}$ + $\dfrac{1}{5}$ – $\dfrac{1}{8}$ +$\dfrac{1}{8}$ – $\dfrac{1}{9}$ + $\dfrac{1}{19}$ -$\dfrac{1}{32}$ + $\dfrac{1}{32}$ – $\dfrac{1}{57}$ + $\dfrac{1}{57}$ – $\dfrac{1}{87}$

    = $\dfrac{1}{3}$ – $\dfrac{1}{87}$

    = $\dfrac{29}{87}$ – $\dfrac{1}{87}$

    = $\dfrac{28}{87}$

   Bài 5 sai đề :v

    

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2. Lời giải:

   4.

   $A=\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+…+\dfrac{1}{24.25}$ 

   $A=(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+…+\dfrac{1}{24}-\dfrac{1}{25})$ 

   $A=(\dfrac{1}{5}-\dfrac{1}{25})$ 

   $A=\dfrac{4}{25}$

   $A=\dfrac{4}{25}$

   ;

   ;

   ;

   `B= 2/3.5 + 3/5.8 + 11/8.19 + 13/19.32 + 25/32.57 + 30/57.87`

   `B=(1/3-1/5)+(1/5-1/8)+(1/8-1/9)+…+(1/32-1/57)+(1/57-1/87)`

   `B=1/3-1/87`

   `B=28/87`

   5.

   `A =10/17 + 8/15 + 11/12`

   `A=286/255 + 11/12`

   `A=693/340`

   Ta có:` A≈2`

   `=>` Vô lí

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