Giải thích các bước giải:
$A=1-\dfrac{3}{4}+(\dfrac{3}{4})^2-(\dfrac{3}{4})^3+(\dfrac{3}{4})^4-...-(\dfrac{3}{4})^{2009}+(\dfrac{3}{4})^{2010}$
$\rightarrow A.(\dfrac{3}{4})^2 = (\dfrac{3}{4})^2-(\dfrac{3}{4})^2+(\dfrac{3}{4})^4-(\dfrac{3}{4})^5+....-(\dfrac{3}{4})^{2011}+(\dfrac{3}{4})^{2012}$
$\rightarrow A.(\dfrac{3}{4})^2-A=-(\dfrac{3}{4})^{2011}+(\dfrac{3}{4})^{2012}-(1-\dfrac{3}{4})$
$\rightarrow A((\dfrac{3}{4})^2-1)=(\dfrac{3}{4})^{2011}(\dfrac{3}{4}-1)+(\dfrac{3}{4}-1)$
$\rightarrow A(\dfrac{3}{4}-1)(\dfrac{3}{4}+1)=((\dfrac{3}{4})^{2011}+1)(\dfrac{3}{4}-1)$
$\rightarrow A(\dfrac{3}{4}+1)=(\dfrac{3}{4})^{2011}+1$
$\rightarrow A.\dfrac{7}{4}=(\dfrac{3}{4})^{2011}+1$
$\rightarrow A=\dfrac{4}{7}((\dfrac{3}{4})^{2011}+1)$
$\rightarrow A$ không là số nguyên
