Question

Rút gọn \(B=\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+\left(-5\right)^3+...+\left(-5\right)^{2016}+\left(-5\right)^{2017}\)

Answer 1

\(B=\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\)

\(-5B=\left(-5\right)^1+\left(-5\right)^2+\left(-5\right)^3+...+\left(-5\right)^{2017}\)

\(-6B=\left(-5\right)^{2017}-1\)

\(B=\frac{\left(-5\right)^{2017}-1}{-6}\)

Answer 2

Ta có : B = (-5)^0 + (-5)^1 + ......+ (-5)^2017

          (-5)B = (-5)^1 + (-5)^2 + .......+ (-5)^2018

              (-4)B = (-5)^0- (-5)^2018

           B = 1 - (-5)^2018 / (-4)

Nếu có sai sót gì mong các bạn bỏ qua

Answer 3

\(-5B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}\)

\(-4B=\left(-5\right)^{2018}-\left(-5\right)^0\)

\(\Rightarrow B=\frac{\left(-5\right)^{2018}-\left(-5\right)^0}{-4}\)

Answer 4

\(B=\left(-5\right)^0+\left(-5\right)^1+................+\left(-5\right)^{2016}+\left(-5\right)^{2017}\)

\(\Rightarrow\left(-5\right)B=\left(-5\right)^1+\left(-5\right)^2+.............+\left(-5\right)^{2017}+\left(-5\right)^{2018}\)

\(\Rightarrow\left(-5\right)B-B=\left[\left(-5\right)^1+\left(-5\right)^2+..........+\left(-5\right)^{2018}\right]\)\(-\left[\left(-5\right)^0+\left(-5\right)^1+..........+\left(-5\right)^{2017}\right]\)

\(\Rightarrow\left(-6\right)B=\left(-5\right)^{2018}-\left(-5\right)^0\)

\(\Rightarrow B=\frac{\left(-5\right)^{2018}-\left(-5\right)^0}{\left(-6\right)}\)

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