Question

1/1.2+1/2.3+....+1/x.(x+1)=996/997

Answer 1

1/1.2 + 1/2.3 + ... + 1/x.(x+1) = 996/997

1 - 1/2 + 1/2 - 1/3 + ... + 1/x - 1/x+1 = 996/997

1 - 1/x+1 = 996/997

1/x+1 = 1 - 996/997

1/x+1 = 1/997

=> x + 1 = 997

          x = 997 - 1

          x = 996

Vậy x = 996

Answer 2

\(=>1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{996}{997}\)

\(=>1-\frac{1}{x+1}=\frac{996}{997}\)

\(=>\frac{x+1-1}{x+1}=\frac{996}{997}\)

\(=>\frac{x}{x+1}=\frac{996}{996+1}\)

=>x=996

Answer 3

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x\left(x+1\right)}=\frac{996}{997}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{996}{997}\)

\(1-\frac{1}{x+1}=\frac{996}{997}\)

         \(\frac{1}{x+1}=1-\frac{996}{997}\)

          \(\frac{1}{x+1}=\frac{1}{997}\)

=> x + 1 = 997

=>       x = 997 - 1

=>       x = 996