<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993

<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993

<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993

<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993

<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993

<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993

<=>2.(1/2-1/x+1)=1991/1993

<=>1/2-1/x+1=1991/1993:2=1991/3986

<=> 1/x+1=1/2-1991/3986=2/3986=1/1993

=>x=1993-1=1992

<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993

<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993

<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993

<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993

<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993

<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993

<=>2.(1/2-1/x+1)=1991/1993

<=>1/2-1/x+1=1991/1993:2=1991/3986

<=> 1/x+1=1/2-1991/3986=2/3986=1/1993

=>x=1993-1=1992

1+13+16+110+...+1x(x+2):2=19911993

⟹12+16+112+120+...+1x(x+2)=19911993.2

⟹11.2+12.3+13.4+14.5+...+1x.(x+2)=19911993.2

⟹1−12+12−13+14−15+...+1x−1x+2=19911993.2

⟹1−1x+2=19913986

⟹1x+2=19913986−1

⟹1x+2=−19953986

⟹x+2=−39861995

⟹x=−79761995
 

<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993

<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993

<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993

<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993

<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993

<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993

<=>2.(1/2-1/x+1)=1991/1993

<=>1/2-1/x+1=1991/1993:2=1991/3986

<=> 1/x+1=1/2-1991/3986=2/3986=1/1993

=>x=1993-1=1992

1+13+16+110+...+1x(x+2):2=19911993

⟹12+16+112+120+...+1x(x+2)=19911993.2

⟹11.2+12.3+13.4+14.5+...+1x.(x+2)=19911993.2

⟹1−12+12−13+14−15+...+1x−1x+2=19911993.2

⟹1−1x+2=19913986

⟹1x+2=19913986−1

⟹1x+2=−19953986

⟹x+2=−39861995

⟹x=−79761995

Ai làm đc giải cụ thể ra nha!thanks

=> 1/2+1/6+1/12+1/20+....+1/x.(x+1) = 1992/1993

=> 1/2+1/2.3+1/3.4+1/4.5+.....+1/x.(x+1) = 1992/1993

=> 1/2+1/2-1/3+1/3-1/4+1/4-1/5+.....+1/x-1/x+1 = 1992/1993

=> 1 - 1/x+1 = 1992/1993

=> x/x+1 = 1992/1993

=> x = 1992

Vậy x = 1992

Tk mk nha

\(\Rightarrow\frac{2}{2}+\frac{2}{2.3}+\frac{2}{2.6}+...+\frac{2}{x\left(x+1\right)}=\frac{3984}{1993}\)

\(\Rightarrow2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{3984}{1993}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{3984}{1993}:2\)

\(\Rightarrow1-\frac{1}{x+1}=\frac{1992}{1993}\)

\(\Rightarrow\frac{x}{x+1}=\frac{1992}{1993}\)

=>x=1992

mina toán 6 sau khó vậy bó tay .com.vn