Find the sum of the series.
-$$\frac { 3 } { 4 } - \frac { 3 ^ { 3 } } { 4 ^ { 3 } \cdot 3 ! } + \frac { 3 ^ { 5 } } { 4 ^ { 5 } \cdot 5 ! } - \frac { 3 ^ { 7 } } { 4 ^ { 7 } \cdot 7 ! } + \ldots$$
A) $\cos \frac { 3 } { 4 }$
B) $\sin \frac { 4 } { 3 }$
C) $\sin \frac { 3 } { 4 }$
D) $\ln \frac { 3 } { 4 }$

Question

Quizplus · Accepted Answer

This is an alternating series with decreasing terms, so we can apply the alternating series test. The limit of the terms as $n$ approaches infinity is 0, so the series converges.

To find the sum, we can use the formula for the sum of an infinite alternating series:

$$S = a_1/(1-r)$$

where $a_1$ is the first term and $r$ is the common ratio of the series. In this case, $a_1 = 3/4$ and $r = -3/16$. Substituting these values, we get:

$$S = \frac{3/4}{1+3/16} = \boxed{	extbf{(C) } \sin \frac{3}{4}}$$

Find the Sum of the Series A) cos⁡34\cos \frac { 3 } { 4 }cos43​

Find the Sum of the Series A) $\cos \frac { 3 } { 4 }$