Question

M=\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{49.50}với1\)

Answer 1

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

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

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

\(M=\frac{49}{50}\)

\(\Rightarrow M<1\)

Answer 2

M=1-1/2+1/2-1/3+...+1/49-1/50

M=1-1/50<1

=>M<1

Answer 3

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

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

 Vậy M < 1

Answer 4

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

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

\(M=\frac{49}{50}\)

\(\Rightarrow M<1\)
 

Answer 5

Ta có:

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

M=\(1-\frac{1}{50}=\frac{49}{80}<1\)

Vậy M<1