a) \(\dfrac{17}{20}< \dfrac{18}{20}< \dfrac{18}{19}\Rightarrow\dfrac{17}{20}< \dfrac{18}{19}\)

b) \(\dfrac{19}{18}>\dfrac{19+2024}{18+2024}=\dfrac{2023}{2022}\Rightarrow\dfrac{19}{18}>\dfrac{2023}{2022}\)

c) \(\dfrac{135}{175}=\dfrac{27}{35}\)

\(\dfrac{13}{17}=\dfrac{26}{34}< \dfrac{26+1}{34+1}=\dfrac{27}{35}\)

\(\Rightarrow\dfrac{13}{17}< \dfrac{135}{175}\)

Ta có :

\(\dfrac{1}{11}>\dfrac{1}{20}\\ \dfrac{1}{12}>\dfrac{1}{20}\\ ..........\\ \dfrac{1}{20}=\dfrac{1}{20}\)

\(\Rightarrow\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{20}>\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}\\ \Rightarrow S>\dfrac{10}{20}\\ \Rightarrow S>\dfrac{1}{2}\)

quy đồng

lấy 36 làm mẫu số chung

-13 / 12 = -39/36

-19/18 = -38/36

mà đối với số dương số nào lớn hơn thì số đó bé hơn 

vậy -39/36 <-38/36

=> -13 / 12 < -19/18 = -38/36

Giải:

\(\dfrac{-13}{12}=-1+\dfrac{-1}{12}\) 

\(\dfrac{-19}{18}=-1+\dfrac{-1}{18}\)

Vì  \(\dfrac{-1}{12}< \dfrac{-1}{18}\) nên \(\dfrac{-13}{12}< \dfrac{-19}{18}\)

Chúc bạn học tốt!

a, \(\dfrac{14}{13}-\dfrac{1}{13}-\dfrac{19}{20}=1-\dfrac{19}{20}=\dfrac{1}{20}\)

b, \(-\dfrac{24}{17}+\dfrac{7}{17}+\dfrac{1}{16}=\dfrac{-17}{17}+\dfrac{1}{16}=-1+\dfrac{1}{16}=-\dfrac{15}{16}\)

\(\dfrac{14}{13}+\left(\dfrac{-1}{13}-\dfrac{19}{20}\right)=\left(\dfrac{14}{13}+\dfrac{-1}{13}\right)-\dfrac{19}{20}=\\ \dfrac{13}{13}-\dfrac{19}{20}=1-\dfrac{19}{20}=\dfrac{20}{20}-\dfrac{19}{20}=\dfrac{1}{20}\)

Câu b em làm tương tự nhé

\(a.\dfrac{14}{13}+\left(\dfrac{-1}{13}+\dfrac{19}{20}\right)=\left(\dfrac{14}{13}+\dfrac{-1}{13}\right)-\dfrac{19}{20}=1+\dfrac{19}{20}=\dfrac{20}{20}-\dfrac{19}{20}=\dfrac{1}{20}\\ b.\dfrac{-24}{17}+\left(\dfrac{-7}{17}-\dfrac{1}{16}\right)=\left(\dfrac{-24}{17}+\dfrac{7}{17}\right)+\dfrac{1}{16}=-1+\dfrac{1}{16}=\dfrac{-16}{16}+\dfrac{1}{16}=\dfrac{-15}{16}\)

Vì 13²⁰+1/13¹⁹+1>1

=>13²⁰+1/13¹⁹+1>13²⁰+1+12/13¹⁹+1+12 

Ta có: 13²⁰+1+12/13¹⁹+12

         = 13²⁰+13/13¹⁹+13

         =13(13¹⁹+1)/13(13¹⁸+1)

        = 13¹⁹+1/13¹⁸+1

 => 13²⁰+1/13¹⁹+1> 13¹⁹+1/13¹⁸+1 

Vậy A<B                              

\(B=\frac{13^{20}+1}{13^{19}+1}>1\)

\(B=\frac{13^{20}+1}{13^{19}+1}>\frac{13^{20}+1+12}{13^{19}+1+12}\)

\(B=\frac{13^{20}+13}{13^{19}+13}=\frac{13\left(13^{19}+1\right)}{13\left(13^{18}+1\right)}\)

\(B=\frac{13^{19}+1}{13^{18}+1}=A\)

\(\Rightarrow B>A\)

Tất cả đọc kĩ lại đi. Đừng có xem qua loa rồi nói tôi như vậy.

`14/13 + ( (-1)/3 - 19/20)`

`= 14/13 + (-1)/3 - 19/20`

`= 13/13 -19/20`

`= 1 -19/20`

`= 20/20 -19/20`

`=1/20`

` 14/13 + ( -1/13 - 19/20 ) ` 

`= (14/13 + (-1)/13) - 19/20 `

`=  1 - 19/20 `

`= 1/20`

\(ta có A=\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{15}}{13^{16}}+1\)=\(\dfrac{1}{13}+1\)

B=\(\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{16}}{13^{17}}+1\)=\(\dfrac{1}{13}+1\)

vậy A=B

\(A=\dfrac{13^{15}+1}{13^{16}+1}vàB=\dfrac{13^{16}+1}{13^{17}+1}\)

ta có

\(\dfrac{13^{16}+1}{13^{17}+1}< 1\Rightarrow\dfrac{13^{16}+1+12}{13^{17}+1+12}=\dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\dfrac{13^{15}+1}{13^{16}+1}=A\)

vậy B<A

\(A=\dfrac{13^{15}+1}{13^{16}+1}vàB=\dfrac{13^{16}+1}{13^{17}+1}\)

ta có B<1 nên

\(\dfrac{13^{16}+1}{13^{17}+1}< \dfrac{13^{16}+1+12}{13^{17}+1+12}=\dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\dfrac{13^{15}+1}{13^{16}+1}=A\)

Vậy B<A

Ta có:\(\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}>4\cdot\dfrac{1}{16}=\dfrac{1}{4}\)

\(\dfrac{1}{17}+\dfrac{1}{18}+\dfrac{1}{19}+\dfrac{1}{20}>4\cdot\dfrac{1}{20}=\dfrac{1}{5}\)

=>\(\dfrac{1}{13}+\dfrac{1}{14}+...+\dfrac{1}{20}>\dfrac{1}{4}+\dfrac{1}{5}=\dfrac{9}{20}\)

=>A>\(\dfrac{1}{12}+\dfrac{9}{20}\)

\(\dfrac{1}{12}>\dfrac{1}{20}\)

=>\(A>\dfrac{1}{20}+\dfrac{9}{20}=\dfrac{1}{2}\)

Vậy...