Question

CHo A=1+4+4 mũ 2+.......+4 mũ 2017 và B=4 mũ 2018:6. Tính 2B-A

Answer 1

\(A=1+4+4^2+...+4^{2017}\)

=>\(4\cdot A=4+4^2+4^3+...+4^{2018}\)

=>\(4A-A=4+4^2+...+4^{2018}-1-4-4^2-...-4^{2017}\)

=>\(3A=4^{2018}-1\)

=>\(A=\dfrac{4^{2018}-1}{3}\)

\(2B-A=\dfrac{4^{2018}}{6}\cdot2-\dfrac{4^{2018}-1}{3}\)

\(=\dfrac{4^{2018}}{3}-\dfrac{4^{2018}-1}{3}=\dfrac{1}{3}\)