Write the sum without sigma notation and evaluate it.
-$$\sum _ { k = 1 } ^ { 3 } ( - 1 ) ^ { k } \sin \frac { 7 \pi } { 2 }$$
A) $- \sin \frac { 7 \pi } { 2 } + \sin \frac { 7 \pi } { 2 } - \sin \frac { 7 \pi } { 2 } = 1$
B) $- \sin \frac { 7 \pi } { 2 } + \sin \frac { 7 \pi } { 2 } - \sin \frac { 7 \pi } { 2 } = 0$
C) $- \sin \frac { 7 \pi } { 2 } + \sin \frac { 7 \pi } { 2 } - \sin \frac { 7 \pi } { 2 } = - 1$
D) $- \sin \frac { 7 \pi } { 2 } - \sin \frac { 7 \pi } { 2 } = 2$

Question

Quizplus · Accepted Answer

The sum can be written as:$$(-1)^1 \sin \frac{7\pi}{2} + (-1)^2 \sin \frac{7\pi}{2} + (-1)^3 \sin \frac{7\pi}{2}$$$$= -\sin \frac{7\pi}{2} + \sin \frac{7\pi}{2} - \sin \frac{7\pi}{2}$$$$= 1$$

Write the Sum Without Sigma Notation and Evaluate It ∑k=13(−1)ksin⁡7π2\sum _ { k = 1 } ^ { 3 } ( - 1 ) ^ { k } \sin \frac { 7 \pi } { 2 }k=1∑3​(−1)ksin27π​

Write the Sum Without Sigma Notation and Evaluate It $\sum _ { k = 1 } ^ { 3 } ( - 1 ) ^ { k } \sin \frac { 7 \pi } { 2 }$