Question

[Nguyen Ba Nha]

Giải hộ mình bài này nha!

1/3+1/6+1/10+...+2/X(X+1)=2007/2019

Answer 1

[duong thi hong nhung]

=>2/2.3+2/3.4+2/4.5+............+2/x.(x+1)=2007/2019

=>2(1/2.3+1/3.4+1/4.5+.......+1/(x+1))=2007/2019

=>2(1/2-1/3+1/3-1/4+1/4-1/5+.....+1/x-1/x+1)=2007/2019

=>2(1/2-1/2x+1)=2007/2019

=>1-2/x+1=2007/2009=>2/x+1=1-2007/2019=12/2019

=>x+1=336,5.Vay x=335,5

Answer 2

[Pé_sun]

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}\)\(=\frac{2007}{2019}\)

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2019}\)

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}\right)\)\(=\frac{2007}{2019}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\)\(=\frac{2007}{2019}\div2\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{669}{1346}\)

\(\frac{1}{x+1}=\frac{1}{2}-\frac{669}{1346}\)

\(\frac{1}{x+1}=\frac{2}{673}\)

\(\frac{2}{\left(x+1\right)2}=\frac{2}{673}\)

\(\Rightarrow\left(x+1\right)2=673\)

\(\Rightarrow x+1=673\div2\Rightarrow x+1=336,5\Rightarrow x=336,5-1=335,5\)