Question

tim x

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

Answer 1

1/3+1/6+.......+2/x(x+1)=2014/2015

=>1x2/3x2+1x2/6x2+.....+2/x(x+1)=2014/2015

=>2/6+2/12+...........+2/x(x+1)=2014/2015

=>2(1/6+1/12+......+1/x(x+1)=2014/2015

=>2(1/2x3+1/3x4+.....+1/x(x+1)=2014/2015

=>2(1/2-1/3+1/3-1/4+.....+1/x-1/x+1=2014/2015

=>2(1/2-1/x+1)=2014/2015

=>1/2-1/x+1=2014/2015:2

=>1/2-1/x+1=1007/2015

=>1/x+1=1/2-1007/2015

=>1/x+1=1/4030

=>x+1=4030

=>x=4030-1

=>x=4029

Answer 2

Quy đồng lên nhé, Nhân với 2 

 = 2/6 + 2/12 + 2/20 +......+ 2/x(x+1)= 2014/ 2015 

= 2 (1/(2.3) + 1/(3.4) + .... +  1/ x.(x+1) ) = 2014 / 2015

Tự làm nốt 

Answer 3

Gọi S= tổng trên

S=2/2.3+2/3.4+2/4.5+...+2/x(x+1)=2014/2015

S=2(1/2.3+1/3.4+1/4.5+...+1/x(x+1))=2014/2015

S=2(1/2-1/x+1)=2014/2015

S=1/2-1/x+1=1007/2015

S=1/x+1=1/4030

suy ra x+1=4030

suy ra x=4029