N = -5/1×3 + -5/3×5 + -5/5×7 +….+ -5/2013×2015

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1. Đáp án:

    

   Giải thích các bước giải:

    $N=$ $\dfrac{-5}{1.3}$ $+$ $\dfrac{-5}{3.5}$ $+$ $\dfrac{-5}{5.7}$ $+…+$ $\dfrac{-5}{2013.2015}$

   $N=$ $\dfrac{-5}{2}$ $($ $\dfrac{1}{1.3}$ $+$ $\dfrac{1}{3.5}$ $+$ $\dfrac{1}{5.7}$ $+…+$ $\dfrac{1}{2013.2015}$  $)$

   $N=$ $\dfrac{-5}{2}$ $($ $1$ $-$ $\dfrac{1}{3}$ $+$ $\dfrac{1}{3}$ $-$ $\dfrac{1}{5}$ $+$ $\dfrac{1}{5}$ $-$ $\dfrac{1}{7}$ $+…+$ $\dfrac{1}{2013.}$ $-$ $\dfrac{1}{2015}$ $)$

   $N=$ $\dfrac{-5}{2}$ $($ $1$ $-$ $\dfrac{1}{2015}$ $)$

   $N=$ $\dfrac{-5}{2}$ $.$ $\dfrac{2014}{2015}$ $)$

   $N=$ $\dfrac{(-5).2014}{2.2015}$ $=$ $\dfrac{(-1).5.1007}{2.5.403}$ 

   $N=$ $\dfrac{-1007}{403}$ 

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2. Đáp án:

    

   Giải thích các bước giải:

   `N=(-5)/(1*3)+(-5)/(3*5)+(-5)/(5*7)+…+(-5)/(2013*2015)`

   `N=(-5)/(2)*((1)/(1*3)+(1)/(3*5)+(1)/(5*7)+…+(1)/(2013*2015))`

   `N=(-5)/(2)*((1)/(1)-(1)/(3)+(1)/(3)-(1)/(5)+(1)/(5)-(1)/(7)+…+(1)/(2013)-(1)/(2015))`

   `N=(-5)/(2)*(1-(1)/(2015))`

   `N=(-5)/(2)*(2014)/(2015)`

   `N=(-1007)/(403)`

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