Question

\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+............+\frac{1}{x\left(x+1\right):2}=1\frac{1991}{1993}\)

Tính tổng

Answer 1

=> 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

Answer 2

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

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

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

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

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

=>x=1992

Answer 3

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Answer 4

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