Write the sum without sigma notation and evaluate it.
-$$\sum _ { k = 1 } ^ { 4 } 2 \sin \frac { \pi } { k }$$
A) $2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 6 + \sqrt { 2 }$
B) $2 \sin \pi + 2 \sin \frac { \pi } { 4 } = \sqrt { 2 }$
C) $2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 2 + \sqrt { 3 } + \sqrt { 2 }$
D) $2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 1 + \frac { \sqrt { 3 } + \sqrt { 2 } } { 2 }$

Question

Quizplus · Accepted Answer

Plugging in the values of k from 1 to 4, we get:
$$2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 0 + 2 + \sqrt{3} + \sqrt{2} = 2 + \sqrt { 3 } + \sqrt { 2 }$$

Write the Sum Without Sigma Notation and Evaluate It ∑k=142sin⁡πk\sum _ { k = 1 } ^ { 4 } 2 \sin \frac { \pi } { k }k=1∑4​2sinkπ​

Write the Sum Without Sigma Notation and Evaluate It $\sum _ { k = 1 } ^ { 4 } 2 \sin \frac { \pi } { k }$