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

question 62

Multiple Choice

Write the sum without sigma notation and evaluate it.
- $$\sum _ { \mathrm { k } = 1 } ^ { 4 } 2 \cos \frac { \pi } { \mathrm { k } }$$

• A) \(2 \cos \pi + 2 \cos \frac { \pi } { 4 } = - 2 + \sqrt { 2 }\)
• B) \(2 \cos \pi + 2 \cos \frac { \pi } { 2 } + 2 \cos \frac { \pi } { 3 } + 2 \cos \frac { \pi } { 4 } = - 1 + \sqrt { 2 }\)
• C) \(2 \cos \pi + 2 \cos \frac { \pi } { 2 } + 2 \cos \frac { \pi } { 3 } + 2 \cos \frac { \pi } { 4 } = - 2 + \sqrt { 3 } + \sqrt { 2 }\)
• D) \(2 \cos \pi + 2 \cos \frac { \pi } { 2 } + 2 \cos \frac { \pi } { 3 } + 2 \cos \frac { \pi } { 4 } = 3 + \sqrt { 2 }\)