Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 6 } \left( 2 i ^ { 2 } - i ^ { 3 } \right)$$

question 493

Multiple Choice

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
- $$\sum _ { i = 1 } ^ { 6 } \left( 2 i ^ { 2 } - i ^ { 3 } \right)$$

• A) 623
• B) \(- 3108\)
• C) \(- 259\)
• D) \(- 1036\)

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Definitions:

Myelination

The process of wrapping axons with myelin, a fatty substance that speeds up the transmission of electrical signals in the nervous system.

Axons

Long, slender projections of nerve cells that transmit electrical impulses away from the neuron's cell body.

Conduction

Transfer of energy, such as heat, from one point to another without evident movement in the conducting body.

Glial Cells

Non-neuronal cells in the central and peripheral nervous system that support and protect neurons.