3 years ago

D FEEDBACK

Mathematics

1 answer:

In-s [12.5K]3 years ago

8 0

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3 years ago

PLEASE HELP!!!

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

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

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