1.Tính
\(E=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(E=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(E=\frac{1}{1}-\frac{1}{50}\)
\(E=\frac{49}{50}\)
Câu 2 mình không biết, xin lỗi nha
E=1/1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50
=1/1-1/50=49/50
1.
\(E=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
\(E=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)
2.
\(x+\frac{1}{6}=\frac{x}{3}\)
\(\frac{1}{6}=\frac{x}{3}-x=x\left(\frac{1}{3}-1\right)\)
\(\frac{1}{6}=-\frac{2}{3}x\Rightarrow x=\frac{1}{6}:-\frac{2}{3}=-\frac{1}{4}\)
a) \(E=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{49\cdot50}\)
\(E=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
\(E=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)
b) \(x+\frac{1}{6}=\frac{x}{3}\)
\(x+\frac{1}{6}=\frac{2x}{6}\)
\(x=\frac{2x}{6}-\frac{1}{6}\)
\(\frac{x}{1}=\frac{2x-1}{6}\)
\(\frac{6x}{6}=\frac{2x-1}{6}\)
\(6x=2x-1\Rightarrow4x=-1\)
\(\Rightarrow x=-\frac{1}{4}\)
