[tex]\bf \textit{sum of an infinite geometric series}\\\\
S=\sum\limits_{i=0}^{\infty}\ a_1r^i\implies \cfrac{a_1}{1-r}\qquad
\begin{cases}
a_1=\textit{first term}\\
r=\textit{common ratio}
\end{cases}[/tex]
[tex]\bf -----------------------------\\\\
\sum\limits_{n=1}^{\infty}\ 1400(-0.5)^{n-1}\qquad
\begin{cases}
a_1=1400\\
r=-0.5\to -\frac{1}{2}
\end{cases}
\\\\\\
\cfrac{1400}{1-\left(-\frac{1}{2} \right)}\implies \cfrac{1400}{1+\frac{1}{2}}\implies \cfrac{1400}{\frac{3}{2}}\implies \cfrac{1400}{1}\cdot \cfrac{2}{3}\implies \cfrac{2800}{3}[/tex]
