Question

Answer 1

\(...\Rightarrow\dfrac{1}{4}C=1+\dfrac{1}{4}+\dfrac{1}{4^2}+...\dfrac{1}{4^{2012}}\)

\(\Rightarrow\dfrac{1}{4}C-C=1-\dfrac{1}{4^{2013}}\)

\(\Rightarrow-\dfrac{3}{4}C=1-\dfrac{1}{4^{2013}}\)

\(\Rightarrow C=\dfrac{1}{3.4^{2012}}-\dfrac{4}{3}=\dfrac{1}{3}\left(\dfrac{1}{4^{2012}}-4\right)< \dfrac{1}{3}\)

\(\Rightarrowđpcm\)

Answer 2

Answer 3

Sửa lại \(...4C-C=3C=1-\dfrac{1}{4^{2013}}\Rightarrow C=\dfrac{1}{3}\left(1-\dfrac{1}{4^{2013}}\right)< \dfrac{1}{3}\)