\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{2010}\)
\(\frac{3}{4}A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3-...-\left(\frac{3}{4}\right)^{2011}\)
\(\frac{3}{4}A-1=-\left[1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{2010}\right]-\left(\frac{3}{4}\right)^{2011}\)
\(\frac{3}{4}A-1=A-\left(\frac{3}{4}\right)^{2011}\)
\(\frac{3}{4}A-A=-\left(\frac{3}{4}\right)^{2011}+1\)
\(-\frac{1}{4}A=1-\left(\frac{3}{4}\right)^{2011}\)
\(A=\frac{1-\left(\frac{3}{4}\right)^{2011}}{-\frac{1}{4}}=1:-\frac{1}{4}-\left(\frac{3}{4}\right)^{2011}:\left(-\frac{1}{4}\right)=-4+3\cdot\left(\frac{3}{4}\right)^{2010}\)
=>A không phải là số nguyên
