Ta có :
\(S=\left(-3\right)^0+\left(-3\right)+\left(-3\right)^2+..................+\left(-3\right)^{2015}\)
\(\Rightarrow\left(-3\right).S=\left(-3\right)+\left(-3\right)^2+\left(-3\right)^3+..............+\left(-3\right)^{2015}+\left(-3\right)^{2016}\)
\(\Rightarrow\left(-3\right).S-S=\left[\left(-3\right)+\left(-3\right)^2+..............+\left(-3^{2015}\right)+\left(-3\right)^{2016}\right]-\left[\left(-3\right)^0+\left(-3\right)+...........+\left(-3\right)^{2015}\right]\)\(\Rightarrow\left(-4\right)S=\left(-3\right)^{2016}-\left(-3\right)^0\)
\(\Rightarrow\left(-4\right).S=\left(-3\right)^{2016}-1\)
\(\Rightarrow S=\dfrac{\left(-3\right)^{2016}-1}{-4}\)
\(\Rightarrow S=\dfrac{3^{2016}-1}{-4}\)