Question

[Yến Nguyễn]

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

Answer 1

[Phạm Tuấn Đạt]

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

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

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

Answer 2

[Doraemon]

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

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

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

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

So sánh \(\frac{49}{50}< 1\)nên \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{49\times50}< 1\)