Question

Tìm x biết :1/3+1/6+1/10+...+2/ x(x+1) =2014/2015

Answer 1

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2014}{2015}\)

\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2014}{2015}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1007}{2015}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1007}{2015}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{4030}\)

=>x+1=4030

=>x=4029

vậy x=4029

Answer 2

1/3+1/6+1/10+...+ 2/X(X+1) = 2014/2016