so sánh 1/20 + 1/21 + 1/22 + …….+ 1/ 50 với 3/4

0 bình luận về “so sánh 1/20 + 1/21 + 1/22 + …….+ 1/ 50 với 3/4”

1. Đáp án:

   Dưới

   Giải thích các bước giải:

   $A=\dfrac{1}{20}+\dfrac{1}{21}+…+\dfrac{1}{50}$

   $⇒A<\dfrac{1}{20}+(\dfrac{1}{21}+…+\dfrac{1}{50})$

   $⇒A<\dfrac{1}{20}+(\dfrac{1}{50}+…+\dfrac{1}{50})$

   $⇒A<\dfrac{1}{20}+30×\dfrac{1}{50}$

   $⇒A<\dfrac{1}{20}+\dfrac{3}{5}$

   $⇒A<\dfrac{13}{20}$

   Vì $\dfrac{13}{20}<\dfrac{15}{20}=\dfrac{3}{4}$

   $⇒A<\dfrac{3}{4}$

   Vậy đpcm

   Trả lời

2. Ta có :

   $\dfrac{1}{20}+\dfrac{1}{21}+\dfrac{1}{22}+…+\dfrac{1}{50}$ 

   $=\dfrac{1}{20}+(\dfrac{1}{21}+\dfrac{1}{22}+..+\dfrac{1}{30})+(\dfrac{1}{31}+\dfrac{1}{32}+…+\dfrac{1}{40})+(\dfrac{1}{41}+\dfrac{1}{42}+…+\dfrac{1}{50})$

   $>\dfrac{1}{20}+(\dfrac{1}{30}+\dfrac{1}{30}+..+\dfrac{1}{30})+(\dfrac{1}{40}+\dfrac{1}{40}+..+\dfrac{1}{40})+(\dfrac{1}{50}+\dfrac{1}{50}+..+\dfrac{1}{50})$

   $=\dfrac{1}{20}+\dfrac{1}{30}\times10+\dfrac{1}{40}\times10+\dfrac{1}{50}\times10$

   $=\dfrac{1}{20}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}$

   $=(\dfrac{1}{20}+\dfrac{1}{5})+\dfrac{1}{3}+\dfrac{1}{4}$

   $=\dfrac{1}{4}+\dfrac{1}{3}+\dfrac{1}{4}$

   $>\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{3}{4}$

   Vậy $A>\dfrac{3}{4}$

   Trả lời