Đáp án: $x=-\dfrac{1}{91}$
Giải thích các bước giải:
Ta có :
$(\dfrac{1}{1.7}+\dfrac{1}{7.13}+\dfrac{1}{13.19}+..+\dfrac{1}{85.91})+125x=-\dfrac{110}{91}$
$\to \dfrac16(\dfrac{6}{1.7}+\dfrac{6}{7.13}+\dfrac{6}{13.19}+..+\dfrac{6}{85.91})+125x=-\dfrac{110}{91}$
$\to \dfrac16(\dfrac{7-1}{1.7}+\dfrac{13-7}{7.13}+\dfrac{19-13}{13.19}+..+\dfrac{91-85}{85.91})+125x=-\dfrac{110}{91}$
$\to \dfrac16(\dfrac11-\dfrac17+\dfrac17-\dfrac1{13}+\dfrac1{13}-\dfrac1{19}+..+\dfrac{1}{85}-\dfrac{1}{91})+125x=-\dfrac{110}{91}$
$\to \dfrac16(1-\dfrac{1}{91})+125x=-\dfrac{110}{91}$
$\to \dfrac16\cdot \dfrac{90}{91}+125x=-\dfrac{110}{91}$
$\to \dfrac{15}{91}+125x=-\dfrac{110}{91}$
$\to 125x=-\dfrac{125}{91}$
$\to x=-\dfrac{1}{91}$
