2009/2010=1-1/2010<1-1/2011=2010/2011

vậy 2009/2010<2010/2011

3^400=(3^4)^100=81^100>64^100=4^300

=>1/3^400<1/4^300

Vậy 1/3^400<1/4^300

mik làm câu A thôi nha

ta có :

1 - 2009/2010 = 1/2010

1 - 2010/2011 = 1/2011

Phần bù nào bé thì phân số đó lớn .

Vì 1/2010 > 1/2011

Nên 2009/2010 > 2010/2011

Ta thấy hiệu giữa mẫu số và tử số của hai phân số bằng nhau ( = 1 ) 
Để so sánh hai phân số, ta so sánh các hiệu. 

\(1-\frac{2009}{2010}\)và \(1-\frac{2010}{2011}\)

Ta có :

\(1-\frac{2009}{2010}=\frac{2010}{2010}-\frac{2009}{2010}=\frac{1}{2010}\)

\(1-\frac{2010}{2011}=\frac{2011}{2011}-\frac{2010}{2011}=\frac{1}{2011}\)

Ta thấy :

\(\frac{1}{2010}>\frac{1}{2011}\)

Hay :

\(1-\frac{2009}{2010}>1-\frac{2010}{2011}\)

Vậy \(\frac{2009}{2010}< \frac{2010}{2011}\)

Ta có : \(\dfrac{200+201}{201+202}=\dfrac{200}{201+202}+\dfrac{201}{201+202}\)

Mà \(\dfrac{200}{201}>\dfrac{200}{201+202}\) ; \(\dfrac{201}{202}>\dfrac{201}{201+202}\)

\(\Rightarrow\dfrac{200}{201}+\dfrac{201}{202}>\dfrac{200+201}{201+202}\)

Ta có \(\dfrac{200+201}{201+202}=\dfrac{200}{201+202}+\dfrac{201}{201+202}\)

Mà \(\dfrac{200}{201}>\dfrac{200}{201+202}\) ; \(\dfrac{201}{202}>\dfrac{201}{201+202}\)

\(\Rightarrow\dfrac{200}{201}+\dfrac{201}{202}>\dfrac{200+201}{201+202}\)

\(A=\frac{199}{200}+\frac{200}{201}+\frac{201}{202}< \frac{199}{200+201+202}+\frac{200}{200+201+202}+\frac{201}{200+201+202}\)

A                                                 \(< \frac{199+200+201}{200+201+202}=B\)

\(A< B\)

Ta có: \(A=\frac{199}{200}+\frac{200}{201}+\frac{201}{202}< \frac{199}{200+201+202}+\frac{200}{200+201+202}+\frac{201}{200+201+202}< \)

                                                              \(< \frac{199+200+201}{200+201+202}\)

Vậy A < B

ỦNG HỘ TỚ NHA

\(\frac{199}{200}>\frac{199}{200+201+202}\)

\(\frac{200}{201}>\frac{200}{200+201+202}\)

\(\frac{201}{202}>\frac{201}{200+201+202}\)

=>\(A>B\)

Do \(\frac{199}{200}\)> \(\frac{199}{200+201+202}\), \(\frac{200}{201}\)>\(\frac{200}{200+201+202}\),\(\frac{201}{202}\)>\(\frac{201}{200+201+202}\)nên A>B

200+201/201+202=200/403+201/403

vì 200/201>200/403

    201/202>201/403 nên \(\frac{200}{201}+\frac{201}{202}>\frac{200+201}{201+202}\)

200+201 hay 200+202

a/\(\frac{\left(2^3.5.7\right).\left(5^2.7^3\right)}{\left(2.5.7^2\right)^2}\)

=\(\frac{2^3.5^3.7^4}{2^2.5^2.7^4}\)

=2.5

=10

nghịch đảo 2 phân số ta có:   \(\frac{2010}{2009}v\text{à}\frac{2011}{2010}\)

 phân tích ra ta có:\(\frac{2010}{2009}=1+\frac{1}{2009}\)

                            \(\frac{2011}{2010}=1+\frac{1}{2010}\)

Vì \(\frac{1}{2009}>\frac{1}{2010}\)

nên \(\frac{2009}{2010}<\frac{2010}{2011}\)

a/ Do : 2009/2010 > 2009/2011, 2009/2011 < 2010/2011 nên 2009/2010 < 2010/2011

a, Ta có\(\)\(\frac{2009}{2010}< \frac{2009}{2011}\)

Mà \(\frac{2009}{2011}< \frac{2010}{2011}\)

Vậy\(\frac{2009}{2010}< \frac{2010}{2011}\)

Ta có :\(\frac{1}{3^{400}}=\frac{1}{\left(3^4\right)^{100}}=\frac{1}{81^{100}}\)

\(\frac{1}{4^{300}}=\frac{1}{\left(4^3\right)^{100}}=\frac{1}{64^{100}}\)

Vì\(\frac{1}{81^{100}}< \frac{1}{64^{100}}\)

Vậy\(\frac{1}{3^{400}}< \frac{1}{4^{300}}\)

c, Ta có : B=\(\frac{200+201}{201+202}=\frac{200}{201+202}+\frac{201}{201+202}\)

\(\Rightarrow\frac{200}{201}>\frac{200}{201+202}\)

\(\frac{201}{202}>\frac{201}{201+202}\)

Vậy A>B

d, Ta có \(A=\frac{2008}{2008\times2009}=\frac{1}{2019}\) 

\(B=\frac{2009}{2009\times2010}=\frac{1}{2010}\)

Vì \(\frac{1}{2009}>\frac{1}{2010}\)

Vậy A>B