Question

So sánh:

\(\frac{2012^{99}+1}{2012^{89}+1}\) và  \(\frac{2012^{100}+1}{2012^{90}+1}\)

Answer 1

Vì \(\frac{2012^{100}+1}{2012^{99}+1}\)<1

=>\(\frac{2012^{100}+1}{2012^{99}+1}\)>\(\frac{2012^{100}+1+2011}{2012^{99}+1+2011}\)

Ta có: \(\frac{2012^{100}+1+2011}{2012^{99}+1+2011}\)=\(\frac{2012^{100}+2012}{2012^{99}+2012}\)=\(\frac{2012\left(2012^{99}+1\right)}{2012\left(2012^{98}+1\right)}\)=\(\frac{2012^{99}+1}{2012^{98}+1}\)

=>\(\frac{2012^{100}+1}{2012^{99}+1}\)>\(\frac{2012^{99}+1}{2012^{98}+1}\)