Hồ Ngọc Minh Châu Võ cho mình hỏi nhưng bài kia mỗi bài 1 dòng hay là cả một bài vậy bạn

1/2^2>1/2.3;1/3^2>1/3.4;......;1/9^2>1/9.10

suy ra  S > 1/2.3+1/3.4+......+1/9.10

            S> 1/2-1/3+1/3-1/4 +.....+1/9-1/10

            S> 1/2-1/10=2/5

Vay 2/5 < S

Vậy còn S < \(\frac{8}{9}\)thì sao, bạn quên chưa chứng minh rồi

=> 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

chuyển 1 đi còn cái kia=1991/1993

nhân mỗi p/số với 1/2 rồi p/tích mẫu=2.3,3.4........x.(x+1)

lập hiệu ra rồi tính OK???

=2/2+2/6+2/12+...+...+2/x(x+1)=3984/1993

=2(1/1.2+1/2.3+1/3.4+...+1/x.(x+1)=3984/1993

=2(1-1/2+1/2-1/3+14-1/5+...+1/x-1/x+1=3984/1993

=2(1-1/x+1)=3984/1993

=2-2/x+1=3984/1993

2/x+1=2/1993

x+1=1003

x=1992

\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{x\left(x+1\right):2}=1\frac{1991}{1993}\)

\(\Rightarrow\frac{1}{3}+\frac{1}{6}+...+\frac{1}{x\left(x+1\right):2}=\frac{1991}{1993}\)

\(\Rightarrow\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=\frac{1991}{1993}\)

\(\Rightarrow\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x\left(x+1\right)}=\frac{1991}{1993}\)

\(\Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1991}{1993}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1991}{3986}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1991}{3986}\)\(\Rightarrow\frac{1}{x+1}=\frac{1}{1993}\)

\(\Rightarrow x+1=1993\Rightarrow x=1992\)

cho e hỏi

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