Question

[Đỗ Nguyễn Như Bình]

5.1/ cho A= 1/2^2+1/3^2+1/4^2+...+1/100^2. Chứng minh rằng A< 3/4.

Answer 1

[Nguyễn Hữu Thế]

\(\Rightarrow A< \frac{1}{1.2}+\frac{1}{2.3}+............+\frac{1}{99.100}\)

\(\Rightarrow A< \frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...........+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A< \frac{1}{1}-\frac{1}{100}\)

\(\Rightarrow A< \frac{99}{100}\)

Mà \(\frac{99}{100}< \frac{3}{4}\)

\(\Rightarrow A< 3\)          ĐPCM

Answer 2

[Đỗ Nguyễn Như Bình]

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