Question

Bài 6:(0,5 điểm) Cho 

Chứng minh A < 2.

Answer 1

\(A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\)

\(A< 1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{49.50}\)

\(A< 1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{50}\)

\(A< 2-\frac{1}{50}< 2\)

Vậy A < 2

Answer 2

\(\Rightarrow A< \frac{1}{1}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}=1+1-\frac{1}{50}=2-\frac{1}{50}< 2\)

\(\Rightarrow A< 2-\frac{1}{50}< 2\) hay \(A< 2\)