Ta có: A < \(\frac{1}{1^2}+\frac{1}{1.2}+...+\frac{1}{49.50}\)
A < \(1+\frac{1}{1.2}+...+\frac{1}{49.50}\)
A < 1 + (1 - 1/50)
A < 1 + 49/50
Vì 1 + 49/50 < 2 nên A < 1 + 49/50 < 2
Vậy A < 2
nếu đúng thì cho mk biết nha
\(\frac{1}{1^2}=1\)
\(\frac{1}{2^2}<\frac{1}{1.2}\)
\(\frac{1}{3^2}<\frac{1}{2.3}\)
.....................
\(\frac{1}{50^2}<\frac{1}{49.50}\)
\(\Rightarrow A<\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)
\(\Rightarrow A<1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
\(\Rightarrow A<1-\frac{1}{50}=\frac{49}{50}\)
mà \(\frac{49}{50}<1=1<2\)
\(\Rightarrow A<2\)
