Tính A = $\frac{10}{56}$ + $\frac{10}{140}$ + $\frac{10}{260}$ + … + $\frac{10}{1400}$

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1. 10/56+10/140+10/260+….+10/1400
   A=5/28+5/70+5/130+….+5/700
   3A/5=3/4.7+3/7.10+3/10.13+…+3/25.28
   3A/5=1/4-1/7+1/7-1/10+1/10-1/13+….+1/25-1/28
   3A/5=1/4-1/28
   3A/5=3/14
   A=3/14.5/3
   A=5/14
   Vậy A=5/14

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2. Đáp án: 5/14

    

   Giải thích các bước giải:

   Ta có: A = 10/56 + 10/140 + 10/260 + …+ 10/1400

   <=> A = 20/8.14 + 20/14.20 + 20/20.26 + …+ 20/50.56

   20/8.14 = (10/3)*(1/8 – 1/14)

   20/14.20 = (10/3)*(1/14 – 1/20)

   20/20.26= (10/3)*(1/20 – 1/26)

   …

   20/50.56 = (10/3)*(1/50 – 1/56)

   => A = (10/3)*(1/8 – 1/14) + (10/3)*(1/14 – 1/20) + (10/3)*(1/20 – 1/26) + …+  (10/3)*(1/50 – 1/56)

   A =  (10/3)*(1/8 – 1/14 + 1/14 – 1/20 + 1/20 – 1/26 + …+  1/50 – 1/56)

   A = (10/3)*(1/8  – 1/56)

   A = (10/3)*(6/56)

   A = 5/14.

    

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