Question

so sánh M = 1/2.1 + 1/2.3+1/2.4+....+1/49.50 với 1 

 

Answer 1

Ta có : 

\(M=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\) ( sai đề nhé ) 

\(M=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(M=1-\frac{1}{50}=\frac{49}{50}< 1\)

Vậy \(M< 1\)

Chúc bạn học tốt ~ 

Answer 2

\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

\(\Rightarrow M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(\Rightarrow M=1-\frac{1}{50}>1\)

\(\RightarrowĐPCM\)

Answer 3

\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{49\times50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}< 1\)

\(\Rightarrow M< 1\)