Giải thích các bước giải:
\(C=\dfrac{5}{4}+\dfrac{5}{4^{2}}+\dfrac{5}{4^{3}}+...+\dfrac{5}{4^{2020}}\)
\(\Leftrightarrow 4C=5+\dfrac{5}{4}+\dfrac{5}{4^{2}}+...+\dfrac{5}{4^{2019}}\)
\(\Rightarrow 4C-C=(5+\dfrac{5}{4}+\dfrac{5}{4^{2}}+...+\dfrac{5}{4^{2019}})-(\dfrac{5}{4}+\dfrac{5}{4^{2}}+\dfrac{5}{4^{3}}+...+\dfrac{5}{4^{2020}})\)
\(\Leftrightarrow 3C=5-\dfrac{5}{4^{2020}}\)
\(\Leftrightarrow 3C<5\)
\(\Leftrightarrow C<\dfrac{5}{3}\)