Question

B=1+3²+3⁴+...+3²⁰¹⁸

Answer 1

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

Answer 2

\(9B=3^2+3^4+...+3^{2020}\)

\(\Leftrightarrow8B=3^{2018}-1\)

\(\Leftrightarrow B=\dfrac{3^{2018}-1}{8}\)

Answer 3

B=1+3²+3⁴+...+3²⁰¹⁸

3B = 3 + 3³ + 3⁵ + .... + 3²⁰¹⁹

3B - B = ( 3 + 3³ + 3⁵ + .... + 3²⁰¹⁹ ) - ( 1+3²+3⁴+...+3²⁰¹⁸ )

2B = 3 + 3²⁰¹⁹ - 1

B = \(\dfrac{3+3^{2019}-1}{2}\)