3 years ago

How would you solve the following problem?

Mathematics

1 answer:

seraphim [82]3 years ago

5 0

The answer should be 1/9y^4

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Topic: Finite Geometric Sums <br> what is the value of ..

kobusy [5.1K]

$\bf \sum\limits_{i=a_1}^{a_n}\ a1\cdot (r)^{n-1}\iff S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\qquad 
\begin{cases}
a_1=\textit{first term}\\
r=\textit{common ratio}\\
n=n^{th}\ term
\end{cases}\\\\
-----------------------------\\\\

\begin{array}{llll}
\sum\limits_{i=1}^{3}\ &4\cdot \left( \frac{1}{2} \right)^{i-1}\\
&\uparrow \quad \uparrow \\
&a_1\quad r
\end{array}\iff S_3=4\left( \cfrac{1-\left( \frac{1}{2} \right)^3}{1-\left( \frac{1}{2} \right)} \right)$