Write the sum without sigma notation and evaluate it.
-$$\sum _ { \mathrm { k } = 1 } ^ { 3 } ( - 1 ) ^ { \mathrm { k } + 1 } \cos 10 \mathrm { k } \pi$$
A) $- \cos 10 \pi + \cos 20 \pi - \cos 30 \pi = - 1$
B) $\cos 10 \pi + \cos 30 \pi = 2$
C) $\cos 10 \pi - \cos 20 \pi + \cos 30 \pi = 1$
D) $\cos 10 \pi - \cos 20 \pi + \cos 30 \pi = - 1$

Question

Quizplus · Accepted Answer

The sum can be written as $\cos 10\pi - \cos 20\pi + \cos 30\pi$. Since $\cos 10\pi = \cos 20\pi = -1$ and $\cos 30\pi = 1$, the sum evaluates to $1$.

Write the Sum Without Sigma Notation and Evaluate It ∑k=13(−1)k+1cos⁡10kπ\sum _ { \mathrm { k } = 1 } ^ { 3 } ( - 1 ) ^ { \mathrm { k } + 1 } \cos 10 \mathrm { k } \pik=1∑3​(−1)k+1cos10kπ

Write the Sum Without Sigma Notation and Evaluate It $\sum _ { \mathrm { k } = 1 } ^ { 3 } ( - 1 ) ^ { \mathrm { k } + 1 } \cos 10 \mathrm { k } \pi$