Question

So sánh 2 biểu thức sau:

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

Answer 1

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

\(5B=\frac{5^{2010}+5}{5^{2010}+1}=1+\frac{4}{5^{2010}+1}\)

\(5B>5A\Rightarrow B>A\)

Answer 2

Ta có:

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

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

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

5B = \(\frac{5^{2010}+5}{5^{2010}+1}\) = \(\frac{5^{2010}+1+4}{5^{2010}+1}\) = 1 + \(\frac{4}{5^{2010}+1}\)

Vì 1 + \(\frac{4}{5^{2011}+1}\) < \(\frac{4}{5^{2010}+1}\) => 5A < 5B

Vì 5A < 5B => A < B