Question

So sánh:

a) A= 100^2009+1/ 100^2008+1

B= 100^2010+1/100^2009+1

b) A= 2003*2004-1/2003*2004

B= 2004*2005-1/2004*2005

Answer 1

a, A<B

b, A>B

       hok tốt

Answer 2

a.A

b.A>B

Answer 3

bạn trình bày hẳn ra

Answer 4

a.A

b.A>B

Answer 5

a) Ta có \(A=\frac{100^{2009}+1}{100^{2008}+1}\)

=> \(\frac{A}{100}=\frac{100^{2009}+1}{100^{2009}+100}=1-\frac{99}{100^{2009}+100}\)

Lại có B = \(\frac{100^{2010}+1}{100^{2009}+1}\)

=> \(\frac{B}{100}=\frac{100^{2010}+1}{100^{2010}+100}=1-\frac{99}{100^{2010}+100}\)

Vì \(\frac{99}{100^{2009}+100}>\frac{99}{100^{2010}+100}\)

=> \(1-\frac{99}{100^{2009}+100}< 1-\frac{99}{100^{2010}+100}\)

=> \(\frac{A}{100}< \frac{B}{100}\Rightarrow A< B\)

b) Ta có A = \(\frac{2003.2004-1}{2003.2004}\)

=> \(A-1=\frac{2003.2004-1-2003.2004}{2003.2004}=\frac{-1}{2003.2004}\)

Lại có B = \(\frac{2004.2005-1}{2004.2005}\)

=> \(B-1=\frac{2004.2005-1-2004.2005}{2004.2005}=\frac{-1}{2004.2005}\)

Vì \(\frac{-1}{2003.2004}>\frac{-1}{2004.2005}\)

=> A - 1 > B - 1

=> A > B