Question

So sánh 

M=1/1.2 + 1/2.3 +...+1/49.50   với 1

Giải ra hộ:😆

Answer 1

\(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{49\cdot50}\)

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

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

Vì \(\frac{49}{50}< 1\)\(\Rightarrow M< 1\)

VẬY M < 1

HK TỐT #

Answer 2

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

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

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

\(\Leftrightarrow M< 1\)

Answer 3

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

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

     \(=1-\frac{1}{50}\)

Mà \(1-\frac{1}{50}< 1\)nên \(M< 1\)

Answer 4

\(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{49\cdot50}\)

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

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

\(< 1\)