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# Chứng minh A=1/1^2+1/2^2+1/3^2+...+1/50^2 < 2

Chứng minh :

A= 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<2

Theo dõi Vi phạm
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## Trả lời (1)

• Ta có: $$\dfrac{1}{1^2}=1$$

$$\dfrac{1}{2^2}< \dfrac{1}{1.2}=1-\dfrac{1}{2}$$

$$\dfrac{1}{3^2}< \dfrac{1}{2.3}=\dfrac{1}{2}-\dfrac{1}{3}$$

..........

$$\dfrac{1}{50^2}< \dfrac{1}{49.50}=\dfrac{1}{49}-\dfrac{1}{50}$$

$$\Rightarrow A< 1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}=1+1-\dfrac{1}{50}=2-\dfrac{1}{50}< 2$$=> đpcm

bởi Nguyễn Tiến 26/12/2018
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