So sánh hai phân số : 

\(\frac{2009.2009+2008}{2009.2009+2009}\)và \(\frac{2009.2009+2009}{2009.2009+2010}\)

A>b

Cách làm: Bạn tách |B ra rồi so sánh với từng ps ở A, sau đó Kết luận

\(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2008}=1-\frac{1}{2009}+1-\frac{1}{2010}+1-\frac{1}{2011}+1+\frac{3}{2008}\)

\(=4+\left(\frac{1}{2008}-\frac{1}{2009}\right)+\left(\frac{1}{2008}-\frac{1}{2010}\right)+\left(\frac{1}{2008}-\frac{1}{2011}\right)>4\)

4 bé hơn

\(\frac{2007}{2008}>\frac{2007}{2008+2009}\\ \frac{2008}{2009}>\frac{2008}{2008+2009}\\ \Rightarrow\frac{2007}{2008}+\frac{2008}{2009}>\frac{2007}{2008+2009}+\frac{2008}{2008+2009}\\ \Rightarrow\frac{2007}{2008}+\frac{2008}{2009}>\frac{2007+2008}{2008+2009}\\ \Rightarrow M>N\)

10^2008+1/10^2009+1<10^2009+1/10^2010+1

10^2008+1/10^2009+1<10^2009+1/10^2010+1

Tớ chỉ biết đáp án thôi 

k cho mk nha 

Thanks

\(2009A=\frac{2009^{2010}+2009}{2009^{2010}+1}=\)\(\frac{2009^{2010}+1+2008}{2009^{2010}+1}=1+\frac{2008}{2009^{2010}+1}\)

\(2009B=\frac{2009^{2009}+2009}{2009^{2009}+1}=\frac{2009^{2009}+1+2008}{2009^{2009}+1}\)\(=1+\frac{2008}{2009^{2009}+1}\)

Vì \(1+\frac{2008}{2009^{2010}+1}< 1+\frac{2008}{2009^{2009}+1}\) \(\Leftrightarrow A< B\)

\(A=\frac{2009^{2009}+1}{2009^{2010}+1}\Rightarrow2009A=\frac{2009^{2010}+2009}{2009^{2010}+1}\)

\(2009A=\frac{2009^{2010}+1}{2009^{2010}+1}+\frac{2008}{2009^{2010}+1}\)

\(2009A=1+\frac{2008}{2009^{2010}+1}\)

..... sory bn mk hơi luwoif chút nên bn tự lm tương tự vs phần B và so sánh nhé!^^

chuan

Dễ thấy:

\(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)

\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)

\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)

=>\(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)

Hay \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008+2009+2010}{2009+2010+2011}\)

Vậy A > B

Ta có \(\left(-2008\right)^{2008}>\left(-2009\right)^{2009}\)

\(\Rightarrow\frac{1}{\left(-2008\right)^{2008}}<\frac{1}{\left(-2009\right)^{2009}}\)

Ta có: Nếu số mũ là chẵn thì số đó là số nguyên dương, mũ lẻ thì là âm 

=> vế trái> vế phải

1/(-2008)^2008>1/(-2009)^2009