Question

A = 1+4+4mũ 2+4 mũ 3+.......+4 mũ 2018

Answer 1

A = 1+4+\(4^2\)+\(4^3\)+...+\(4^{2018}\)

4.A = 4+ \(4^2\)+\(4^3\)+\(4^4\)+...+\(4^{2019}\)

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A = 1+4+\(4^2\)+\(4^3\)+...+\(4^{2018}\)

3A = \(4^{2019}\)-1

Answer 2

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

\(\Rightarrow4A=4+4^2+4^3+...+4^{2019}\)

\(\Rightarrow4A-A=\left(4+4^2+4^3+...+4^{2019}\right)-\left(1+4+4^2+...+4^{2018}\right)\)

\(\Rightarrow3A=4^{2019}-1\)

\(\Rightarrow A=\frac{4^{2019}-1}{3}\)

Vậy  \(A=\frac{4^{2019}-1}{3}\)

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