\(\dfrac{19}{19}\) = 1 < \(\dfrac{2005}{2004}\) vậy \(\dfrac{19}{19}\) < \(\dfrac{2005}{2004}\)

\(\dfrac{72}{73}\) = 1 - \(\dfrac{1}{73}\) 

\(\dfrac{98}{99}\) = 1 - \(\dfrac{1}{99}\)

Vì \(\dfrac{1}{73}\) > \(\dfrac{1}{99}\) nên \(\dfrac{72}{73}\) < \(\dfrac{98}{99}\) 

1) 19/19 < 2005/2004

2)72/73 > 98/99

\(C-D=\dfrac{\left(98^{99}+1\right)\left(98^{88}+1\right)-\left(98^{89}+1\right)\left(98^{98}+1\right)}{\left(98^{89}+1\right)\left(98^{88}+1\right)}\)

\(=\dfrac{98^{187}+98^{99}+98^{88}+1-98^{197}-98^{89}-98^{98}-1}{\left(98^{89}+1\right)\left(98^{88}+1\right)}\)

\(=\dfrac{98^{99}-98^{98}+98^{88}-98^{89}}{\left(98^{89}+1\right)\left(98^{88}+1\right)}=\dfrac{98^{98}\left(98-1\right)-98^{88}\left(98-1\right)}{\left(98^{89}+1\right)\left(98^{88}+1\right)}\)

\(=\dfrac{97.98^{98}-97.98^{88}}{\left(98^{89}+1\right)\left(98^{88}+1\right)}=\dfrac{97.98^{88}\left(98^{10}-1\right)}{\left(98^{89}+1\right)\left(98^{88}+1\right)}>0\)

\(\Rightarrow C>D\)

`A=3/4+8/9+.............+9999/10000`

`=1-1/4+1-1/9+,,,,,,,,,,+1-1/10000`

`=99-(1/4+1/9+.........+1/10000)<99-0=99`

`=>A<99`

 địt mẹ con ngu t khinh

Giải:

\(A=\dfrac{3}{4}+\dfrac{8}{9}+\dfrac{15}{16}+...+\dfrac{9999}{10000}\) 

\(A=\left(1-\dfrac{1}{4}\right)+\left(1-\dfrac{8}{9}\right)+\left(1-\dfrac{1}{16}\right)+...+\left(1-\dfrac{1}{10000}\right)\) 

\(A=99-\left(\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{19}+...+\dfrac{1}{10000}\right)< 99\) 

\(\Rightarrow A< 99\left(đpcm\right)\) 

Chúc bạn học tốt!

Ta có :

( 98⁴ )³ = 98^4*3 = 98¹²

Vì 98 = 98

mà 12 < 15

Nên 98¹² < 98¹⁵

Hay ( 98⁴ )³ < 98¹⁵

Vậy (98⁴)³ < 98¹⁵

ta có 1/-4003<0<75/106

=>  1/-4003<75/106

106/204>107/206

 so sánh bằng phân số trung gian

vì \(\frac{106}{204}\)> \(\frac{106}{206}\)nên \(\frac{106}{204}\)> \(\frac{107}{206}\)

1) Phân tích A ra :

 A= 17¹⁷.17+\(\frac{1}{17^{18}.17}\)+1 So sánh với B ta có: A có 17¹⁸>17¹⁷ của B nhưng B lại có 1/17¹⁸>1/17¹⁹.

Mà 17¹⁸>1/17¹⁸ nên suy ra A>B

2) Bài nay tương tự bài trên. 

2/(2012+2013) < 2/(2012 + 2012) = 2/ (2.2012) = 1/2012 
2009/(2012+2013) < 2009/2012 

=> 2011/(2012+2013) = 2/(2012+2013) + 2009/(2012+2013) < 1/2012 + 2009/2012 
=> 2011/(2012+2013) < 2010/2012 (a) 

2012/(2012+2013) < 2012/2013 (b) 

lấy (a) + (b) => (2011+2012)/(2012+2013) < 2010/2012 + 2012/2013 

vậy B < A 

trung nguyên làm bài j vậy