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

Đáp án:

Giải thích các bước giải:

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

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

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

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

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

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

$N=$ $\dfrac{-1007}{403}$