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) \(2 \cos \pi + 2 \cos \frac { \pi } { 2 } + 2 \cos \frac { \pi } { 3 } + 2 \cos \frac { \pi } { 4 } = 3 + \sqrt { 2 }\)

Understand the methods used to assess personality traits, including factor analysis and empirically derived testing.

Understand the initial reluctance of the French to support the American Revolution and the factors that eventually swayed their decision.

Grasp the ideological underpinnings of republicanism as envisioned by the patriots.

Recognize the diverse challenges the colonists faced in pursuing full independence.

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