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

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}

Zybrea Knight · Accepted Answer

Final Answer : C, Explanation :   Using the formula for the sum of a finite geometric series with first term $a$ and common ratio $r$, we have:   \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}   Therefore, the best choice is $\boxed{	extbf{(C)}}$.

Find the partial sum. $i−1\sum_{i=1}^{4} 2\left(\frac{3}{2}\right) ^{i-1}$

A) $1054\frac{105}{4}$
B) $174\frac{17}{4}$
C) $654\frac{65}{4}$
D) $894\frac{89}{4}$
E) $794\frac{79}{4}$

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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​

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Learning Objectives

Learning Objectives

Related questions

Find the partial sum. $i−1\sum_{i=1}^{4} 2\left(\frac{3}{2}\right) ^{i-1}$

A) $1054\frac{105}{4}$
B) $174\frac{17}{4}$
C) $654\frac{65}{4}$
D) $894\frac{89}{4}$
E) $794\frac{79}{4}$