[tex]\bf \qquad \qquad \textit{sum of an infinite geometric serie}
\\\\
S_n=\sum\limits_{i=1}^{\infty}\ a_1\cdot r^{i-1}\implies S=\cfrac{a_1}{1-r}\quad
\begin{cases}
a_1=\textit{first term's value}\\
r=\stackrel{0\ \textless \ |r|\ \textless \ 1}{\textit{common ratio}}
\end{cases}[/tex]
[tex]\bf \sum\limits_{n=1}^{\infty}~3\left(\frac{1}{4} \right)^{n-1}~~
\begin{cases}
a_1=3\\
r=\frac{1}{4}
\end{cases}\implies S=\cfrac{3}{1-\frac{1}{4}}\implies S=\cfrac{\quad 3\quad }{\frac{3}{4}}
\\\\\\
S=\cfrac{\underline{3}}{1}\cdot \cfrac{4}{\underline{3}}\implies S=4[/tex]
