\(A=1+\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+..........+\frac{1}{50.50}\)
\(< 1+\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{49.50}\)
\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{49}-\frac{1}{50}\)
\(=1+\frac{49}{50}=1\frac{49}{50}\)
vì\(1\frac{49}{50}< 2\Rightarrow A< 2\)
Giúp mình nha ai nhanh nhất mình sẽ tích cho
\(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}< 1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
mà \(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=2-\frac{1}{50}< 2\)
=> đpcm
