find the sum of the first 100 term of the geometric series with the first term 5 and the common ratio is -2

find the sum of the first 100 term of the geometric series with the first term 5 and the common ratio is -2

$$\\\small{ \begin{array}{rccl} s_{100} &=& \textcolor[rgb]{1,0,0}{5}+&5(-2)^1+5(-2)^2+5(-2)^3+5(-2)^4+\dots+5(-2)^{98}+5(-2)^{99} }\\\\ (-2)s_{100}&=& & 5(-2)^1+5(-2)^2+5(-2)^3+5(-2)^4+\dots+5(-2)^{98}+5(-2)^{99}+\textcolor[rgb]{1,0,0}{5(-2)^{100}} }\\\\ \hline s_{100}-(-2)s_{100}&=& 5-&5(-2)^{100}\\\\ s_{100}+2s_{100}&=& 5-&5(-2)^{100}\\\\ 3s_{100}&=& 5-&5(-2)^{100}\\\\ \end{array} }\\\\ \small \begin{array}{rcl} s_{100} &=& \dfrac{ 5-5(-2)^{100} } {3}\\\\ s_{100} &=& -2112751000380382335827838675625 \end{array} }$$