Câu hỏi của Makoto Haru

Question

tìm x biết :(1/1.2.3+1/2.3.4+1/3.4.5+..........+1/98.99.100).x=-3

Lê Thái Khả Hân · Accepted Answer

$\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{98.99.100}\right)x=-3$

$\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\right)x=-3$

$\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{9900}\right)x=-3$

$\dfrac{1}{2}.\dfrac{4949}{9900}x=-3$

$\dfrac{4949}{19800}x=-3$

$x=-3:\dfrac{4949}{19800}$

$x=-\dfrac{59400}{4949}$Câu trả lời: $\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{98.99.100}\right)x=-3$

$\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\right)x=-3$

$\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{9900}\right)x=-3$

$\dfrac{1}{2}.\dfrac{4949}{9900}x=-3$

$\dfrac{4949}{19800}x=-3$

$x=-3:\dfrac{4949}{19800}$

$x=-\dfrac{59400}{4949}$

Đại số lớp 6