Đáp án+giải thích các bước giải:
Ta có:
$\dfrac{2^{2011}+1}{2^{2010}+1}$
= $\dfrac{2^{2010+1}+1}{2^{209+1}+1}$
= $\dfrac{2^{2010}. 2^{1}+1}{2^{2009}. 2^{1}+1}$
= $\dfrac{2^{2010}. 2+1}{2^{2009}. 2+1}$
= $\dfrac{2^{2010}+1}{2^{2009}+1}$
$do$ $\dfrac{2^{2010}+1}{2^{2009}+1}$ = $\dfrac{2^{2010}+1}{2^{2009}+1}$
⇒ $\dfrac{2^{2011}+1}{2^{2010}+1}$ = $\dfrac{2^{2010}+1}{2^{2009}+1}$
