Find the partial sum. $\sum_{i=1}^{4} 2\left(\frac{3}{2}\right)^{i-1}$
A) $\frac{105}{4}$
B) $\frac{17}{4}$
C) $\frac{65}{4}$
D) $\frac{89}{4}$
E) $\frac{79}{4}$

Question

Quizplus · Accepted Answer

Using the formula for the sum of a finite geometric series with first term $a$ and common ratio $r$, we have:
\begin{align*}
\sum_{i=1}^{4} 2\left(\frac{3}{2}ight)^{i-1} &= 2\left(\frac{3}{2}ight)^0 + 2\left(\frac{3}{2}ight)^1 +2\left(\frac{3}{2}ight)^2 +2\left(\frac{3}{2}ight)^3\
&= 2+3+4.5+6.75 \
&= \frac{65}{4}
\end{align*}
Therefore, the best choice is $\boxed{	extbf{(C)}}$.

Find the Partial Sum ∑i=142(32)i−1\sum_{i=1}^{4} 2\left(\frac{3}{2}\right)^{i-1}∑i=14​2(23​)i−1 A) 1054\frac{105}{4}4105​ B) 174\frac{17}{4}417​ C) 654\frac{65}{4}465​ D) 894\frac{89}{4}489​ E) 794\frac{79}{4}479​

Find the Partial Sum $\sum_{i=1}^{4} 2\left(\frac{3}{2}\right)^{i-1}$ A) $\frac{105}{4}$ B) $\frac{17}{4}$ C) $\frac{65}{4}$ D) $\frac{89}{4}$ E) $\frac{79}{4}$