A= 1/17+ 7/17.27 + 7/27.37 + ……………….. +7/1997.2007

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1. Giải thích các bước giải:

   $\dfrac{1}{17}+\dfrac{7}{17.27}+\dfrac{7}{27.37}+…..+\dfrac{7}{1997.2007}$$=\dfrac{1}{17}+\dfrac{7}{17.27}+\dfrac{7}{27.37}+…..+\dfrac{7}{1997.2007}$

   $=\dfrac{1}{17}+\dfrac{7}{10}.\dfrac{10}{17.27}+\dfrac{7}{10}.\dfrac{10}{27.37}+…..+\dfrac{7}{10}.\dfrac{10}{1997.2007}$

   $=\dfrac{1}{17}+\dfrac{7}{10}.(\dfrac{1}{17}-\dfrac{1}{27})+\dfrac{7}{10}.(\dfrac{1}{27}-\dfrac{1}{37})+…..+\dfrac{7}{10}.(\dfrac{1}{1997}-\dfrac{1}{2007})$

   $=\dfrac{1}{17}+\dfrac{7}{10}.(\dfrac{1}{17}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{37}+…..+\dfrac{1}{1997}-\dfrac{1}{2007})$

   $=\dfrac{1}{17}+ \dfrac{7}{10}.(\dfrac{1}{17}-\dfrac{1}{2007})$

   $=\dfrac{1}{17}+ \dfrac{7}{10}.\dfrac{1}{17}-\dfrac{7}{10.2007}$

   $=\dfrac{1}{17}.(1+ \dfrac{7}{10})-\dfrac{7}{20070}$

   $=\dfrac{1}{17}.\dfrac{17}{10}-\dfrac{7}{20070}$

   $=\dfrac{1}{10}-\dfrac{7}{20070} $

   $=\dfrac{200}{2007}$

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