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

question 197

Multiple Choice

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

• A) \(2 \sin \pi + 2 \sin \frac { \pi } { 4 } = \sqrt { 2 }\)
• B) \(2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 1 + \frac { \sqrt { 3 } + \sqrt { 2 } } { 2 }\)
• C) \(2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 6 + \sqrt { 2 }\)
• D) \(2 \sin \pi + 2 \sin \frac { \pi } { 2 } + 2 \sin \frac { \pi } { 3 } + 2 \sin \frac { \pi } { 4 } = 2 + \sqrt { 3 } + \sqrt { 2 }\)

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Definitions:

K

The chemical symbol for Potassium, an essential dietary mineral and electrolyte involved in nerve function, muscle contraction, and fluid balance.

HA

Depending on context, this can refer to Hyaluronic Acid, a molecule involved in skin hydration and cellular functions, or Hemagglutinin, a protein on the surface of influenza viruses responsible for binding the virus to the host cell.

pH

A measurement system designed to determine the level of acidity or alkalinity in water-based solutions, marked on a continuum from 0 to 14.

K

In the context of chemistry, often represents the equilibrium constant, symbolizing the ratio of product concentrations to reactant concentrations at equilibrium.