so sánh 2/3^2 + 2/3^4 +..+ 2/3^100 với 1/4

Giải thích các bước giải:

$\begin{array}{l}
A = \dfrac{2}{{{3^2}}} + \dfrac{2}{{{3^4}}} + … + \dfrac{2}{{{3^{100}}}}\\
 \Rightarrow \dfrac{1}{{{3^2}}}A = \dfrac{2}{{{3^4}}} + \dfrac{2}{{{3^6}}} + … + \dfrac{2}{{{3^{102}}}}\\
 \Rightarrow A – \dfrac{1}{{{3^2}}}A = \dfrac{2}{{{3^2}}} – \dfrac{2}{{{3^{102}}}}\\
 \Leftrightarrow \dfrac{8}{9}A = \dfrac{2}{9} – \dfrac{2}{{{3^{102}}}}\\
 \Leftrightarrow A = \dfrac{1}{4} – \dfrac{1}{{{{4.3}^{100}}}}\\
 \Rightarrow A < \dfrac{1}{4}
\end{array}$

Ta có đpcm