Question

1+(-3)^2+(-3)^3+...+(-3)^2022

Answer 1

Sửa đề: \(1+\left(-3\right)+\left(-3\right)^2+\cdots+\left(-3\right)^{2022}\)

Đặt \(A=1+\left(-3\right)+\left(-3\right)^2+\cdots+\left(-3\right)^{2022}\)

=>\(\left(-3\right)\cdot A=\left(-3\right)+\left(-3\right)^2+\cdots+\left(-3\right)^{2023}\)

=>\(\left(-3\right)\cdot A-A=\left(-3\right)+\left(-3\right)^2+\ldots+\left(-3\right)^{2023}-1-\left(-3\right)-\left(-3\right)^2-\cdots-\left(-3\right)^{2022}\)

=>\(-4\cdot A=\left(-3\right)^{2023}-1=-3^{2023}-1\)

=>\(A=\frac{3^{2023}+1}{4}\)