Question

Answer 1

\(B=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2020}}+\dfrac{1}{3^{2021}}\)

=>\(3B=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2019}}+\dfrac{1}{3^{2020}}\)

=>\(3B-B=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{2019}}+\dfrac{1}{3^{2020}}-\dfrac{1}{3}-\dfrac{1}{3^2}-\dfrac{1}{3^3}-...-\dfrac{1}{3^{2021}}\)

=>\(2B=1-\dfrac{1}{3^{2021}}\)

=>\(B=\dfrac{1}{2}-\dfrac{1}{2\cdot3^{2021}}< \dfrac{1}{2}\)