Question

So sánh:

A= 5^2013-3/5^2014+1

B= 5^2015-3/5^2016+1

Answer 1

Mik đang cần gấp nhé!

Answer 2

Ta có \(A=\frac{5^{2013}-3}{5^{2014}+1}\)

\(\Rightarrow5A=\frac{5^{2014}-15}{5^{2014}+1}=\frac{5^{2014}+1-16}{5^{2014}+1}=1-\frac{16}{5^{2014}+1}\)

Ta có \(B=\frac{5^{2015}-3}{5^{2016}+1}\)

\(\Rightarrow5A=\frac{5^{2016}-15}{5^{2016}+1}=\frac{5^{2016}+1-16}{5^{2016}+1}=1-\frac{16}{5^{2015}+1}\)

Ta thấy \(5^{2014}+1< 5^{2016}+1\Rightarrow\frac{16}{5^{2014}+1}>\frac{16}{5^{2016}+1}\)

Do đó \(1-\frac{16}{5^{2014}+1}< 1-\frac{16}{5^{2016}+1}\)hay \(5A< 5B\)

Khi đó A < B