2001/2002 lớn hơn

phần bù đến 1 của 2000/2001 là 1- 2000/2001=1/2001

phần bù đến 1 của 2001/2002 là 1-2001/2002=1/2002

Vì 1/2001>1/2002 nên 2000/2001<2001/2002

1- \(\frac{2000}{2001}\)= \(\frac{1}{2001}\)

1 - \(\frac{2001}{2002}\)=  \(\frac{1}{2002}\)

Vì \(\frac{1}{2001}\)< \(\frac{1}{2002}\)nên \(\frac{2000}{2001}\)< \(\frac{2001}{2002}\)

So sánh giữa 2000/2001 và 2001/2002

1 - 2000/2001 = 1/2001

1- 2001/2002 = 1/2002

Vì 1/2001 > 1/2002 nên 2000/2001 > 2001/2002

ta có:

1-\(\frac{2000}{2001}\)=\(\frac{2001}{2001}\)-\(\frac{2000}{2001}\)=\(\frac{1}{2002}\)

và 1- \(\frac{2001}{2002}\)=\(\frac{2002}{2002}\)-\(\frac{2001}{2002}\)=\(\frac{1}{2002}\)

vì \(\frac{1}{2001}\)> \(\frac{1}{2002}\)nên\(\frac{2000}{2001}\)<\(\frac{2001}{2002}\)

Ta có : \(\hept{\begin{cases}\frac{2000}{2001}=\frac{2001}{2001}-\frac{1}{2001}=1-\frac{1}{2001}\\\frac{2001}{2002}=\frac{2002}{2002}-\frac{1}{2002}=1-\frac{1}{2002}\end{cases}\Rightarrow}\frac{2000}{2001}< \frac{2001}{2002}\)

Ta có : 

31/95 = 31 : 95 = 0,326...

2012/6035 = 2012 : 6035 = 0,333...

Lại có : 0,326... < 0,333...

=> 31/95 < 2012/6035

2001/2000 > 2002/2001

j

o

2001/2000=1+1/2000

2002/2001=1+1/2001

Mà 1/2000>1/2001

=>1+1/2000>1+1/2001

hay 2001/2000>2002/2001

Ta có : 

1 - 2000/2001 = 1/2001 

1 - 2001/2002 = 1/2002 

Vì 1/2001 > 1/2002 nên 2000/2001 > 2001/2002

Ta có: \(17A=17.\left(\frac{17^{2001}+1}{17^{2002}+1}\right)=\frac{17^{2002}+17}{17^{2002}+1}=\frac{17^{2002}+1+16}{17^{2002}+1}=1+\frac{16}{17^{2002}+1}\)

\(17B=17.\left(\frac{17^{2000}+1}{17^{2001}+1}\right)=\frac{17^{2001}+17}{17^{2001}+1}=\frac{17^{2001}+1+16}{17^{2001}+1}=1+\frac{16}{17^{2001}+1}\)

Vì 1 = 1 và 16 = 16 nên so sánh mẫu:

17²⁰⁰² + 1 > 17²⁰⁰¹ + 1

=> \(1+\frac{16}{17^{2002}+1}<1+\frac{16}{17^{2001}+1}\)

=> 17A < 17B

=> A < B.

Ta có:\(17^{2001}>17^{2000},1=1\) Còn \(\frac{1}{17^{2002}},\frac{1}{17^{2001}}\) thì ko quan trọng chúng đều nhỏ hơn 1

Nên A>B

ta có:\(A=\frac{2000}{2001}+\frac{2001}{2002}<\frac{2000}{2002}+\frac{2001}{2002}=\frac{2000+2001}{2002}<\frac{2000+2001}{2001+2002}=B\)

\(\Rightarrow A

ta có:\(B=\frac{2000+2001}{2001+2002}=\frac{2000}{2001+2002}+\frac{2001}{2001+2002}\)

vì \(\frac{2000}{2001}>\frac{2000}{2001+2002}và\frac{2001}{2002}>\frac{2001}{2001+2002}\)

\(\Rightarrow\frac{2000}{2001}+\frac{2001}{2002}>\frac{2000+2001}{2001+2002}\)

=>A>B