Question

[hyduyGF]

Bài 6:(0,5 điểm) Cho 

Chứng minh A < 2.

Answer 1

[Dũng Nguyễn Đình]

Ta có :

\(\frac{1}{1^2}< \frac{1}{1.2};\frac{1}{2^2}< \frac{1}{2.3};...;\frac{1}{50^2}< \frac{1}{49.50}\)

\(\Leftrightarrow\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=1-\frac{1}{50}< 1< 2\)

Vậy A < 2

Answer 2

[Lovers]

\(\frac{1}{1^2}=1\)

\(\frac{1}{2^2}< \frac{1}{1.2}\)

\(\frac{1}{3^2}< \frac{1}{2.3}\)

\(...\)

\(\frac{1}{50^2}< \frac{1}{49.50}\)

\(\Rightarrow\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

\(\Rightarrow A< 1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

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

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

Vậy \(A< 2\)