Question

So sánh M = \(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+.......+\(\dfrac{1}{49.50}\) với 1

Answer 1

Ta có: \(M=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\)

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

\(\Rightarrow M=1-\dfrac{1}{50}< 1\)

Vậy M < 1.

Answer 2

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

Vậy M=\(\dfrac{49}{50}\)

*Trước dấu = là 1 chữ M

Answer 3

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

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

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

\(\Rightarrow M< 1\)

\(Vậy\) \(M< 1\)