\(A=\dfrac{14^{14}+1}{14^{15}+1}\)

\(\Rightarrow14.A=\dfrac{14^{15}+14}{14^{15}+1}\)

\(\Rightarrow14.A=\dfrac{14^{15}+1}{14^{15}+1}+\dfrac{13}{14^{15}+1}\)

\(\Rightarrow14.A=1+\dfrac{13}{14^{15}+1}\)

\(B=\dfrac{14^{15}+1}{14^{16}+1}\)

\(\Rightarrow14.B=\dfrac{14^{16}+14}{14^{16}+1}\)

\(\Rightarrow14.B=\dfrac{14^{16}+1}{14^{16}+1}+\dfrac{13}{14^{16}+1}\)

\(\Rightarrow14.B=1+\dfrac{13}{14^{16}+1}\)

Nhận xét: \(\dfrac{13}{14^{15}+1}>\dfrac{13}{14^{16}+1}\) (cùng tử, xét mẫu)

\(\Rightarrow A>B\)

Vậy \(A>B\)

Ta có

Ta có: \(\dfrac{2002}{2003}< \dfrac{14}{13}\) vì \(\dfrac{2002}{2003}< 1\), \(\dfrac{14}{13}>1\)

ta có

2002/2003<1<14/13

=>2002/2003<14/13

\(\dfrac{1}{4444}< 1,\dfrac{3}{7}< 1,\dfrac{9}{5}>1,\dfrac{7}{3}>1,\dfrac{14}{15}< 1,\dfrac{16}{16}=1,\dfrac{14}{11}>1\)

1/4 < 1

3/7 < 1

9/5 > 1

7/3 > 1

14/15 < 1

16/16 = 1

14/11 >1

ta có : `12/14 = 6/7`

`13/24=(13xx7)/(24xx7)= 91/168`

`6/7=(6xx24)/(7xx24)= 144/168`

mà : `91<144`

`=> 13/24 < 12/14`

\(\dfrac{13}{24}\) = \(\dfrac{13\times7}{24\times7}\) = \(\dfrac{91}{168}\)

\(\dfrac{12}{14}\) = \(\dfrac{12\times12}{14\times12}\) = \(\dfrac{144}{168}\)

\(\dfrac{91}{689}< \dfrac{144}{168}\)

\(\dfrac{13}{24}\) < \(\dfrac{12}{14}\)

\(\dfrac{14}{21};\dfrac{60}{72}\)

\(\dfrac{60}{72}=\dfrac{5}{6}=\dfrac{5\cdot21}{6\cdot21}=\dfrac{105}{126}\)

\(\dfrac{14}{21}=\dfrac{14\cdot6}{21\cdot6}=\dfrac{84}{126}\)

\(\dfrac{84}{123}< \dfrac{105}{126}\Rightarrow\dfrac{14}{21}< \dfrac{60}{72}\)

\(\dfrac{38}{133};\dfrac{129}{344}\)

\(\dfrac{38}{133}=\dfrac{19}{7}=\dfrac{19\cdot8}{7\cdot8}=\dfrac{152}{56}\)

\(\dfrac{129}{344}=\dfrac{3}{8}=\dfrac{3\cdot7}{8\cdot7}=\dfrac{21}{56}\)

\(\dfrac{152}{56}>\dfrac{21}{56}\Rightarrow\dfrac{38}{133}>\dfrac{129}{344}\)

`17/20 = 119/140`

`11/14=110/140`

`=> 119/140 > 110/140`

`=> 17/20 > 11/14`

\(\dfrac{17}{20}=\dfrac{17\cdot14}{20\cdot14}=\dfrac{238}{280}\)

\(\dfrac{11}{14}=\dfrac{11\cdot20}{14\cdot20}=\dfrac{220}{280}\)

mà 238>220

nên \(\dfrac{17}{20}>\dfrac{11}{14}\)

a) \(\dfrac{5}{9}< \dfrac{7}{9}\)

b) \(\dfrac{7}{6}>\dfrac{6}{6}\)

c) \(\dfrac{3}{14}< \dfrac{5}{14}\)

d) \(\dfrac{5}{8}< \dfrac{9}{8}\)

a) ta có: 125^4=(5^3)^4=5^12

             49^6= (7^2)^6= 7^12

 vì....>.....=>......>.........

B VÀ C LM TƯƠNG TỰ NHÉ LINH

3111 và 1714 Ta thấy 31^11 < 32^11 = (2^5)^11 = 2^55 (1) 17^14 > 16^14 = (2^4 )^14 = 2^56 (2) Từ (1) và (2) 31^11 < 2^55 < 2^56 < 17^14 nên 31^11 < 17^14

 

a) \(\dfrac{-1}{20}=\dfrac{-7}{140}\)

\(\dfrac{5}{7}=\dfrac{100}{140}\)

mà -7<100

nên \(-\dfrac{1}{20}< \dfrac{5}{7}\)

b) \(\dfrac{216}{217}< 1\)

\(1< \dfrac{1164}{1163}\)

nên \(\dfrac{216}{217}< \dfrac{1164}{1163}\)

c) \(\dfrac{-12}{17}=\dfrac{-180}{255}\)

\(\dfrac{-14}{15}=\dfrac{-238}{255}\)

mà -180>-238

nên \(-\dfrac{12}{17}>\dfrac{-14}{15}\)

d) \(\dfrac{27}{29}>0\)

\(0>-\dfrac{2727}{2929}\)

nên \(\dfrac{27}{29}>-\dfrac{2727}{2929}\)