Tính: B=1/10×9 + 1/18×13 + 1/26×17 +…+ 1/802×405

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1. Đáp án: $B=\dfrac2{81}$

   Giải thích các bước giải:

   Ta có:
   $B=\dfrac{1}{10\cdot 9}+\dfrac{1}{18\cdot13}+\dfrac{1}{26\cdot 17}+…+\dfrac{1}{802\cdot 405}$

   $\to \dfrac12B=\dfrac{1}{10\cdot 9\cdot2}+\dfrac{1}{18\cdot13\cdot2}+\dfrac{1}{26\cdot 17\cdot2}+…+\dfrac{1}{802\cdot 405\cdot2}$

   $\to \dfrac12B=\dfrac{1}{10\cdot 18}+\dfrac{1}{18\cdot26}+\dfrac{1}{26\cdot 34}+…+\dfrac{1}{802\cdot 810}$

   $\to 4B=\dfrac{8}{10\cdot 18}+\dfrac{8}{18\cdot26}+\dfrac{8}{26\cdot 34}+…+\dfrac{8}{802\cdot 810}$

   $\to 4B=\dfrac{18-10}{10\cdot 18}+\dfrac{26-18}{18\cdot26}+\dfrac{34-26}{26\cdot 34}+…+\dfrac{810-802}{802\cdot 810}$

   $\to 4B=\dfrac1{10}-\dfrac1{18}+\dfrac1{18}-\dfrac{1}{26}+\dfrac1{26}-\dfrac1{34}+…+\dfrac1{802}-\dfrac1{810}$
   $\to 4B=\dfrac1{10}-\dfrac{1}{810}$

   $\to 4B=\dfrac8{81}$

   $\to B=\dfrac2{81}$

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2. Đáp án:

   $B=2/81$

   Giải thích các bước giải:

   $1/2B=1/10x9x2+1/18x13x2+1/26x17x2+…+1/802x405x2$

   $1/2B=1/10×18+1/18×26+1/26×34+…+1/802×810$

   $4B=18−10/10×18+26−18/18×26+34−26/26×34+…+810−802/802×810$

   $4B=1/10−1/810$

   $B=(1/10−1/810):4$

   $B=2/81$

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