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

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

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

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

Vậy B < A ( bài này chủ yếu so sánh hai phân số cùng từ, phân số nào có mẫu lớn hơn thì phân số đó nhỏ hơn )

Nếu là so sánh thì B>A vì mỗi phân số của B đều lớn hơn 1 và B nhiều số hạng hơn còn A thì kém về 2 mặt.

Chúc em học tốt^^

Ta có:\(\frac{200}{201}>\frac{200}{201+202}và\frac{201}{202}>\frac{201}{201+202}\)

Suy ra\(\frac{200}{201}+\frac{201}{202}>\frac{200}{201+202}+\frac{201}{201+202}=\frac{200+201}{201+202}\)

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

Ta co:\(\frac{200+201}{201+202}=\frac{200}{201+202}+\frac{201}{201+202}\)

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

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

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

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

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

\(hnhaminhhlai\)

200+201 hay 200+202

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

vì 200/201>200/403

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

\(A=\frac{17^{201}+1}{17^{202}+1}< 1\)

\(\rightarrow A=\frac{17^{201}+1}{17^{202}+1}< \frac{17^{201}+1+16}{17^{202}+1+16}\)

\(\rightarrow A=\frac{17^{201}+1}{17^{202}+1}< \frac{17^{201}+17}{17^{202}+17}\)

\(\rightarrow A=\frac{17^{201}+1}{17^{202}+1}< \frac{17\left(17^{200}+1\right)}{17\left(17^{201}+1\right)}\)

\(\rightarrow A=\frac{17^{201}+1}{17^{202}+1}< \frac{17^{200}+1}{17^{201}+1}\)

\(\rightarrow A=\frac{17^{201}+1}{17^{202}+1}< B\)

\(\rightarrow A< B\)

GIẢI GIÙM MÌNH NHA:THANKS:)

\(\frac{x+199}{200}+\frac{x+198}{201}+\frac{x+197}{202}=-3\)

\(\frac{x+199}{200}+1+\frac{x+198}{201}+1+\frac{x+197}{202}+1=0\)

\(\frac{x+399}{200}+\frac{x+399}{201}+\frac{x+399}{202}=0\)

\(\left(x+399\right)\left(\frac{1}{200}+\frac{1}{201}+\frac{1}{202}\right)=0\)

Mà \(\left(\frac{1}{200}+\frac{1}{201}+\frac{1}{202}\right)\ne0\)

=> x + 399 = 0

=> x = -399 

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

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

\(A=\frac{54.107-53}{53.107+54}=\frac{\left(53+1\right)107-53}{53.107+54}=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)

\(B=\frac{135.269-133}{134.269+135}=\frac{\left(134+1\right)269-133}{134.269+135}=\frac{134.269+269-133}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)

Vậy A<B

câu a là

200/201+201/202>200/202+201/202>1 

200+201/201+201<1

=>200/201+201/202>1>200+201/201+202