Math help

S₁₂ for the series 1 + 1.5 + 2.25 + 3.375 +

$\begin{array}{|rcll|} \hline && 1 + 1.5 + 2.25 + 3.375 +\ldots \\ &=& 1 + 1.5 + 1.5^2 + 1.5^3 + 1.5^4 + 1.5^5 + \ldots \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline A = s_{12} = &=& 1 + 1.5 + 1.5^2 + 1.5^3 + 1.5^4 + 1.5^5 +\ldots + 1.5^{10} + 1.5^{11} \\ B = 1.5\cdot s_{12} = &=& 1.5 + 1.5^2 + 1.5^3 + 1.5^4 + 1.5^5 + 1.5^6 +\ldots + 1.5^{11} + 1.5^{12} \\ B-A = 1.5\cdot s_{12}-s_{12} = &=& 1.5^{12} -1 \\ s_{12}\cdot (1.5-1)&=& 1.5^{12} -1 \\ s_{12}\cdot 0.5&=& 1.5^{12} -1 \\ s_{12} &=& \frac{1.5^{12} -1}{0.5} \\\\ s_{12} &=& \frac{128.746337891}{0.5} \\\\ \mathbf{ s_{12}} &\mathbf{=}& \mathbf{257.492675781\ldots} \\ \hline \end{array}$

The common ratio  = 1.5....so.....

S₁₂ =  [1 - (1.5)^12] / [ 1 - 1.5]  = 257.49267578125