Express the Sum Using Summation Notation $$a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$$

question 40

Multiple Choice

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
- $$a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$$

• A) \(\sum _ { \mathrm { k } = 1 } ^ { 15 } a r ^ { \mathrm { k } }\)
• B) \(\sum _ { k = 0 } ^ { 15 } a r ^ { k }\)
• C) \(\sum _ { \mathrm { k } = 1 } ^ { 16 } a \mathrm { r } ^ { \mathrm { k } }\)
• D) \(\sum _ { k = 0 } ^ { 15 } ( a r ) ^ { k }\)

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Definitions:

Peculiar Ideas

Thoughts or beliefs that are unusual or atypical, sometimes reflecting creativity or innovation, but in other contexts may suggest delusional thinking or disorders.

Obsessive-compulsive

Pertaining to a disorder characterized by intrusive thoughts (obsessions) and repetitive behaviors (compulsions) as a response to these thoughts.

Antisocial

Exhibiting behaviors that violate social norms and can negatively affect others, often associated with a lack of consideration or concern for the well-being of others.

Borderline

Often referring to Borderline Personality Disorder, a mental health condition characterized by mood swings, unstable relationships, self-image issues, and impulsive behavior.