Question

So sánh: A = \(\frac{2005^{2005}+1}{2005^{2006}+1}\) và B = \(\frac{2005^{2004}+1}{2005^{2005}+1}\)

GIÚP MIK NHA MAI THI ÒI

Answer 1

\(10A=\frac{2005^{2006}+10}{2005^{2006}+1}\)

\(10B=\frac{2005^{2005}+10}{2005^{2005}+1}\)

Rồi bạn so sánh 10A và 10B là ra.

Ai thấy đúng thì ủng hộ nha !!!, sai thì góp ý cho mink nha 

Answer 2

Ta có

A <\(\frac{2005^{2005}+2005}{2005^{2006}+2005}=\frac{2005\left(2005^{2004}+1\right)}{2005\left(2005^{2005}+1\right)}\)=\(\frac{2005^{2004}+1}{2005^{2005}+1}\)

\(\RightarrowĐPCM\)

Answer 3

\(A=\frac{2005.\left(2005^{2005}+1\right)}{2005^{2006}+1}=\frac{2005^{2006}+2005}{2005^{2006}+1}=\frac{2005^{2006}+1+2004}{2005^{2006}+1}=1+\frac{2004}{2005^{2006}+1}\)

\(B=\frac{2005.\left(2005^{2004}+1\right)}{2005^{2005}+1}=\frac{2005^{2005}+2005}{2005^{2005}+1}=\frac{2005^{2005}+1+2004}{2005^{2005}+1}=1+\frac{2004}{2005^{2005}+1}\)

Vì  \(2005^{2005}+1< 2005^{2006}+1\)

\(\Rightarrow\frac{2004}{2005^{2005}+1}>\frac{2004}{2005^{2006}+1}\Rightarrow2005B>2005A\Rightarrow B>A\)

Answer 4

mai thi hạ yên tâm mik sẽ giúp bạn 

\(\frac{2005^{2005}+1}{2005^{2004}+1}\)< \(\frac{2005^{2005}+2005}{2005^{2006}+2005}\)= \(\frac{2005.\left(2005^{2004}+1\right)}{2005.\left(2005^{2005}+1\right)}\)= \(\frac{2005^{2004}+1}{2005^{2005}+1}\)( vế B ) 

vậy A < B

Answer 5

Ta có:

\(A=\frac{2005^{2005}+1}{2005^{2006}+1}\)

\(2005\times A=\frac{2005^{2006}+2005}{2005^{2006}+1}\)

\(2005\times A=\frac{2005^{2006}+1+2004}{2005^{2006}+1}\)

\(2005\times A=1+\frac{2004}{2005^{2006}+1}\)

Ta lại có:

\(B=\frac{2005^{2004}+1}{2005^{2005}+1}\)

\(2005\times B=\frac{2005^{2005}+2005}{2005^{2005}+1}\)

\(2005\times B=\frac{2005^{2005}+1+2004}{2005^{2005}+1}\)

\(2005\times B=1+\frac{2004}{2005^{2005}+1}\)

Nhìn vào trên, suy ra A < B