\(\frac{x+18}{2018}+\frac{x+17}{2017}+\frac{x+16}{2016}=3\)

\(\Rightarrow\frac{x+18}{2018}-1+\frac{x+17}{2017}-1+\frac{x+16}{2016}-1=3-3\)

\(\Rightarrow\frac{x+18-2018}{2018}+\frac{x+17-2017}{2017}+\frac{x+16-2016}{2016}=0\)

\(\Rightarrow\frac{x-2000}{2018}+\frac{x-2000}{2017}+\frac{x-2000}{2016}=0\)

\(\Rightarrow\left(x-2000\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\right)=0\)

Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\ne0\)

=> x - 2000 = 0

=> x            = 2000

Ta có : 

\(\frac{x+18}{2018}+\frac{x+17}{2017}+\frac{x+16}{2016}=3\)

\(\Leftrightarrow\)\(\left(\frac{x+18}{2018}-1\right)+\left(\frac{x+17}{2017}-1\right)+\left(\frac{x+16}{2016}-1\right)=3-3\) ( trừ hai vế cho 3 ) 

\(\Leftrightarrow\)\(\frac{x-2000}{2018}+\frac{x-2000}{2017}+\frac{x-2000}{2016}=0\)

\(\Leftrightarrow\)\(\left(x-2000\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\right)=0\)

Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\ne0\)

Nên \(x-2000=0\)

\(\Rightarrow\)\(x=2000\)

Vậy \(x=2000\)

Chúc bạn học tốt ~ 

\(A=1\dfrac{1}{15}.1\dfrac{1}{16}.1\dfrac{1}{17}......1\dfrac{1}{2016}.1\dfrac{1}{2017}\)

\(A=\dfrac{16}{15}.\dfrac{17}{16}.\dfrac{18}{17}......\dfrac{2017}{2016}.\dfrac{2018}{2017}\)

\(A=\dfrac{16.17.18......2017.2018}{15.16.17......2016.2017}\)

\(A=\dfrac{2018}{15}\)

Ta có: \(1\times\frac{1}{15}\times1\frac{1}{16}\times1\frac{1}{17}\times......\times1\frac{1}{2016}\times1\frac{1}{2017}\)

     \(=\frac{1}{15}\times\frac{17}{16}\times\frac{18}{17}\times......\times\frac{2017}{2016}\times\frac{2018}{2017}\)

     \(=\frac{1}{15}\times\frac{2018}{16}\)

     \(=\frac{1009}{8\times15}\)

     \(=\frac{1009}{120}\)

Mình nghĩ đề bài của bạn bị nhầm ở chỗ  \(1\frac{1}{15}\)thành \(1\times\frac{1}{15}\)

Nhưng không sao bạn ạ

Vẫn giải được

\(1\frac{1}{15}\times1\frac{1}{16}\times.....\times1\frac{1}{2017}\)(lỗi đề sao bạn)

\(=\frac{16}{15}\times\frac{17}{16}\times.....\times\frac{2018}{2017}\)

\(=\frac{16\times17\times.....\times2018}{15\times16\times.....\times2017}\)

\(=\frac{2018}{15}\)

nhanh nhanh nha nha tui đâng cần gấp đó nha nha nhanh nha

a) \(\frac{x+1}{5}+\frac{x+1}{6}+\frac{x+1}{7}=\frac{x+1}{8}+\frac{x+1}{9}\)

\(\Leftrightarrow\frac{x+1}{5}+\frac{x+1}{6}+\frac{x+1}{7}-\frac{x+1}{8}-\frac{x+1}{9}=0\)

\(\Leftrightarrow\left(x+1\right).\left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}-\frac{1}{8}-\frac{1}{9}\right)=0\)

\(\Leftrightarrow x+1=0\)

\(\Leftrightarrow x=0-1\)

\(\Rightarrow x=-1\)

Vậy \(x=-1.\)

Mình chỉ làm câu a) thôi nhé.

Chúc bạn học tốt!

Lê Thị Thục HiềnTrần Thanh PhươngVũ Minh Tuấn?Amanda?Nguyễn Việt LâmHISINOMA KINIMADONguyễn Huy TúAkai Haruma

bạn có thể vào câu hổi tương tự hoặc sear google

ahjhj =.="

\(1\frac{1}{15}\cdot1\frac{1}{16}\cdot1\frac{1}{17}\cdot...\cdot1\frac{1}{2016}\cdot1\frac{1}{2017}\)

\(=\frac{16^{\left(1\right)}}{15}\cdot\frac{17^{\left(1\right)}}{16^{\left(1\right)}}\cdot\frac{18^{\left(1\right)}}{17^{\left(1\right)}}\cdot...\cdot\frac{2017^{\left(1\right)}}{2016^{\left(1\right)}}\cdot\frac{2018}{2017^{\left(1\right)}}\)

\(=\frac{1}{15}\cdot2018\)

\(=\frac{2018}{15}=134\frac{8}{15}\)

\(1\cdot\frac{1}{15}\cdot1\frac{1}{16}\cdot1\frac{1}{17}\cdot....\cdot1\frac{1}{2016}\cdot1\frac{1}{2017}\)

\(=\frac{1}{15}\cdot\frac{17}{16}\cdot\frac{18}{17}\cdot....\cdot\frac{2017}{2016}\cdot\frac{2018}{2017}\)

\(=\frac{1}{15}\cdot\frac{1}{16}\cdot2018\)

Dấu "." là dấu nhân nhé bn! phần còn lại bn làm tiếp nha