A=1/1.2+1/2.3+...1/x =49/50
A=1-1/2+1/2-1/3+...+1/x-1-1/x=49/50
A=1-1/x=49/50
A=50/50-1=x=49/50
x=1/50
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{x}=\frac{49}{50}\)
\(\Rightarrow\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{x\left(x-1\right)}=\frac{49}{50}\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x-1}-\frac{1}{x}=\frac{49}{50}\)
\(\Rightarrow1-\frac{1}{x}=\frac{49}{50}\)
\(\Rightarrow\frac{1}{x}=\frac{1}{50}\)
\(\Rightarrow x=50\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{x}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{\left(n-1\right)n}\) với \(\left(n-1\right)n=x\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n-1}-\frac{1}{n}\)
\(A=1-\frac{1}{n}\)
Mà \(A=\frac{49}{50}\)
\(\Rightarrow1-\frac{1}{n}=\frac{49}{50}\)
\(\frac{1}{n}=1-\frac{49}{50}\)
\(\frac{1}{n}=\frac{1}{50}\)
\(\Rightarrow n=50\)
Có \(x=\left(n-1\right)n\)
\(\Rightarrow x=\left(50-1\right)50\)
\(x=49.50\)
\(x=2450\)
