1) $A = \dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2020}}$
$⇒9A = 1+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2018}}$
$⇒9A - A = 1-\dfrac{1}{3^{2020}} $
$⇒8A =\dfrac{3^{2020}-1}{3^{2020}} $
$⇒ A = \dfrac{3^{2020}-1}{8.3^{2020}} = \dfrac{1}{8} -\dfrac{1}{8.3^{2020}} < \dfrac{1}{8}$
$⇒A<\dfrac{1}{8}$
