Question

[nguyen ngoc son]

1.so sánh

a)cho A=\(\frac{10^{2001}+1}{10^{2002}+1}\) ; B=\(\frac{10^{2002}+1}{10^{2003}+1}\) hãy so sánh A và B

b)C=\(\frac{196}{197}+\frac{197}{198}\) và D=\(\frac{196+197}{197+198}\)

c)E=\(\frac{2011+2012}{2012+2013}\) và F=\(\frac{2011}{2012}+\frac{2012}{2013}\)

Answer 1

[Trần Hoàng Anh]

a)

\(10A=\frac{10^{2002}+10}{10^{2002}+1}=1+\frac{9}{10^{2002}+1}\)

\(10B=\frac{10^{2003}+10}{10^{2003}+1}=1+\frac{9}{10^{2003}+1}\)

=> 10A > 10B => A > B