Question

[Hắc Lê Hoàng Linh]

SO SÁNH A= 2005²⁰⁰⁵ +1/2005²⁰⁰⁶+1 và  B =2005²⁰⁰⁴+1/2005²⁰⁰⁵+ 1

Answer 1

[tran thanh minh]

Xét A trước ta có 

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

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

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

Xét B ta có 

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

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

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

ta có vì 2005A<2005B

từ đó suy ra A<B

 nhớ **** đó