Question

A = \(\frac{5^{2010}+1}{5^{2011}+1}\)và B =\(\frac{5^{2009}+1}{5^{2010}+1}\)

so sánh

giúp mình với

Answer 1

Ta có :

\(B=\frac{5^{2009}+1}{5^{2010}+1}=\frac{\left(5^{2009}+1\right).10}{\left(5^{2010}+1\right).10}=\frac{5^{2010}+10}{5^{2011}+10}\)

Ta thấy :

\(5^{2010}=5^{2010};1< 10\Rightarrow5^{2010}+1< 5^{2010}+10\)

\(5^{2011}=5^{2011};1< 10\Rightarrow5^{2011}+1< 5^{2011}+10\)

Suy ra : \(A< B\)

Vậy \(A< B\)

Answer 2

\(A< 1\)

\(A< \frac{5^{2010}+1}{5^{2011}+1}\)

\(A< \frac{5^{2010}+1+4}{5^{2011}+1+4}\)

\(A< \frac{5^{2010}+5}{5^{2011}+5}\)

\(A< \frac{5\left(5^{2009}+1\right)}{5\left(5^{2010}+1\right)}\)

\(A< \frac{5^{2009}+1}{5^{2010}+1}\)

\(A< B\)