Câu hỏi của Linh Chi

Question

cho A= 1/101 + 1/102 + 1/03 + ... + 1/200

chứng minh A > 7/12

Agust D_ · Accepted Answer

Ta có :

$\dfrac{1}{101}>\dfrac{1}{150}$

$\dfrac{1}{102}>\dfrac{1}{150}$

$.............$

$\dfrac{1}{150}=\dfrac{1}{150}$

$\Rightarrow\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{150}>\dfrac{1}{150}+\dfrac{1}{150}+...+\dfrac{1}{150}$( 50 số hạng ) $=\dfrac{1}{3}$

Ta có :

$\dfrac{1}{151}>\dfrac{1}{200}$

$\dfrac{1}{152}>\dfrac{1}{200}$

$..............$

$\dfrac{1}{200}=\dfrac{1}{200}$

$\Rightarrow\dfrac{1}{151}+\dfrac{1}{152}+...+\dfrac{1}{200}>\dfrac{1}{200}+\dfrac{1}{200}+...+\dfrac{1}{200}$( có 50 số hạng ) $=\dfrac{1}{4}$

$\Rightarrow\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{200}>\dfrac{1}{3}+\dfrac{1}{4}$

$\Rightarrow A>\dfrac{7}{12}$

잘 공부하십시오 !Câu trả lời: Ta có :

$\dfrac{1}{101}>\dfrac{1}{150}$

$\dfrac{1}{102}>\dfrac{1}{150}$

$.............$

$\dfrac{1}{150}=\dfrac{1}{150}$

$\Rightarrow\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{150}>\dfrac{1}{150}+\dfrac{1}{150}+...+\dfrac{1}{150}$( 50 số hạng ) $=\dfrac{1}{3}$

Ta có :

$\dfrac{1}{151}>\dfrac{1}{200}$

$\dfrac{1}{152}>\dfrac{1}{200}$

$..............$

$\dfrac{1}{200}=\dfrac{1}{200}$

$\Rightarrow\dfrac{1}{151}+\dfrac{1}{152}+...+\dfrac{1}{200}>\dfrac{1}{200}+\dfrac{1}{200}+...+\dfrac{1}{200}$( có 50 số hạng ) $=\dfrac{1}{4}$

$\Rightarrow\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{200}>\dfrac{1}{3}+\dfrac{1}{4}$

$\Rightarrow A>\dfrac{7}{12}$

잘 공부하십시오 !

Chương III : Phân số