Question

Tổng \(S=\left(-\dfrac{1}{5}\right)^0+\left(-\dfrac{1}{5}\right)^1+\left(-\dfrac{1}{5}\right)^2+...+\left(-\dfrac{1}{5}\right)^{2021}\)có giá trị là

Answer 1

Theo kinh nghiệm của tui thì.......mấy cái bài này hay dễ ra kết quả = 1 với = 0 nhiều lắm:)

Answer 2

\(S=\left(-\dfrac{1}{5}\right)^0+\left(-\dfrac{1}{5}\right)^1+...+\left(-\dfrac{1}{5}\right)^{2021}\)

\(\Rightarrow\left(-\dfrac{1}{5}\right)S=\left(-\dfrac{1}{5}\right)^1+\left(-\dfrac{1}{5}\right)^2+...+\left(-\dfrac{1}{5}\right)^{2021}+\left(-\dfrac{1}{5}\right)^{2022}\)

\(\Rightarrow S-\left(-\dfrac{1}{5}\right)S=\left(-\dfrac{1}{5}\right)^0-\left(-\dfrac{1}{5}\right)^{2022}\)

\(\Rightarrow\dfrac{6}{5}S=1-\dfrac{1}{5^{2022}}\)

\(\Rightarrow S=\dfrac{5}{6}\left(1-\dfrac{1}{5^{2022}}\right)\)