1/ 1.4+ 1/ 4.7+ 1/ 7.10+....+1/ x.( x+ 3)= 672/ 2017
(3/1.4+3/4.7+3/7.10+...+ 3/x(x+3)).1/3=672/2017
(1/1-1/4+1/4-1/7+1/7-1/10+.....+(x+3)-x/x.(x+3)).1/3=672/2017
(1/1-1/(x+3)).1/3=672/2017
1/1-1/(x+3)= 672/2017:1/3
1/1-1/(x+3) = 2016/2017
1/(x+3)=1/1-2016/2017
1/(x+3)=1/2017
x+3=2017
x= 2017-3
x= 2014
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\(\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+...+\frac{1}{x\cdot\left(x+3\right)}=\frac{672}{2017}\)
\(\Rightarrow\frac{1}{3}\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+...+\frac{3}{x\cdot\left(x+3\right)}\right)=\frac{672}{2017}\)
\(\Rightarrow\frac{1}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{672}{2017}\)
\(\Rightarrow\frac{1}{3}\cdot\left(1-\frac{1}{x+3}\right)=\frac{672}{2017}\Rightarrow1-\frac{1}{x+3}=\frac{672}{2017}:\frac{1}{3}\)
\(\Rightarrow1-\frac{1}{x+3}=\frac{672}{2017}\cdot3=\frac{2016}{2017}\Rightarrow\frac{1}{x+3}=1-\frac{2016}{2017}\)
\(\Rightarrow\frac{1}{x+3}=\frac{2017}{2017}-\frac{2016}{2017}\Rightarrow\frac{1}{x+3}=\frac{1}{2017}\)
\(\Rightarrow x+3=2017\Rightarrow x=2017-3\Rightarrow x=2014\)
\(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{x.\left(x+3\right)}=\frac{627}{2017}\\ =>\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{627}{2017}\\ =>\frac{1}{3}\left(1-\frac{1}{x+3}\right)=\frac{627}{2017}\\ =>1-\frac{1}{x+3}=\frac{1881}{2017}\)
=>1/x+3=136/2017
.... thôi mỏi tay quá bạn tự làm tiếp đi(ps:bài tớ làm chưa chắc đúng)