For the given geometric sequence, find the limit of the infinite series, if it exists.
-$\frac{3}{2} \cdot\left(\frac{1}{2}\right)^{n-1}$
A) 3
B) No limit
C) $\frac{3}{2}$
D) 1

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = \frac{3}{2}$ and common ratio $r = \frac{1}{2}$. The sum of an infinite geometric series exists and is given by $S = \frac{a}{1 - r}$ if $|r| < 1$. Here, $|r| = \frac{1}{2} < 1$, so the sum exists and is $S = \frac{\frac{3}{2}}{1 - \frac{1}{2}} = 3$.

For the Given Geometric Sequence, Find the Limit of the Infinite