Question

[Trần Đàm Bảo Hân]

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

Answer 1

[Nguyễn Xuân Sáng]

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

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

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

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

\(\Rightarrow M<1\)

Answer 2

[Kalluto Zoldyck]

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

M = \(1-\frac{1}{50}\)

M = \(\frac{49}{50}<1\)

=> M < 1