Express the Sum Using Summation Notation $$a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$$

question 288

Multiple Choice

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
- $$a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$$

• A) \(\sum _ { \mathrm { k } = 0 } ^ { 11 } \mathrm { ar } ^ { \mathrm { k } }\)
• B) \(\sum _ { k = 1 } ^ { 12 } a r ^ { k }\)
• C) \(\sum _ { \mathrm { k } = 0 } ^ { 11 } ( \mathrm { ar } ) ^ { \mathrm { k } }\)
• D) \(\sum _ { k = 1 } ^ { 11 } a r ^ { k }\)

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Definitions:

Altruistic Punishment

A behavior where individuals punish others for breaking societal norms, even at a cost to themselves, to enforce cooperative behavior.

Cheat The System

Engaging in dishonest or unethical practices to gain an advantage or bypass rules.

Accountability

The obligation or willingness to accept responsibility for one's actions and decisions.

Anonymity

The state of being anonymous, where an individual's identity is unknown or unacknowledged.