Question

PLEASE HELP!!!

Answer 1

$\bf \qquad \qquad \textit{sum of an infinite geometric serie} \\\\ S_n=\sum\limits_{i=1}^{\infty}\ a_1\cdot r^{i-1}\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\textit{first term's value}\\ r=\stackrel{0\ \textless \ |r|\ \textless \ 1}{\textit{common ratio}} \end{cases}$

$\bf \sum\limits_{n=1}^{\infty}~3\left(\frac{1}{4} \right)^{n-1}~~ \begin{cases} a_1=3\\ r=\frac{1}{4} \end{cases}\implies S=\cfrac{3}{1-\frac{1}{4}}\implies S=\cfrac{\quad 3\quad }{\frac{3}{4}} \\\\\\ S=\cfrac{\underline{3}}{1}\cdot \cfrac{4}{\underline{3}}\implies S=4$

Answer 2

I believe the answer is A.