Find the value of ( 0.75 )^31 - 0.75 + [ 0.75 + ( 0.75 )^2 + 1 ]

Answer: Option A

$$\begin{array}{rl}& \text{According to the question,}\\ & \frac{{\left(0.75\right)}^3}{1-0.75}+\left[0.75+{\left(0.75\right)}^2+1\right]\\ & \Rightarrow \frac{{\left(0.75\right)}^3}{1-0.75}+\frac{1^3-{\left(0.75\right)}^3}{1-0.75}\\ & \left[\because a^3-b^3=\left(a-b\right)\left(a^2+b^2+ab\right)\right]\\ & \Rightarrow \frac{{\left(0.75\right)}^3+1-{\left(0.75\right)}^3}{0.25}\\ & \Rightarrow \frac{1}{0.25}\\ & \Rightarrow 4\end{array}$$