Find a Formula for the Nth Partial Sum of the Series

question 57

Multiple Choice

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
- $$3 - 24 + 192 - 1536 + \ldots + ( - 1 ) ^ { n - 1 } 3 \cdot 8 ^ { n - 1 } + \ldots$$

• A) \(\frac { 3 \left( 1 - ( - 8 ) ^ { n } \right) } { 1 - 8 } ; \frac { 3 } { 7 }\)
• B) \(\frac { 3 \left( 1 - ( - 8 ) ^ { n } \right) } { 1 + 8 }\); series diverges
• C) \(\frac { 3 \left( 1 - ( - 8 ) ^ { n } \right) } { 8 - 1 } ;\) series diverges
• D) \(\frac { 3 \left( 1 - ( - 8 ) ^ { n } \right) } { 1 + 8 } ; \frac { 1 } { 3 }\)

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Definitions:

Felony

A serious crime usually punishable by imprisonment for more than one year or by death.

Misdemeanor

A crime that is less serious than a felony and is punishable by a fine and/or imprisonment for less than one year.

Probable Cause

A reasonable ground for belief in the existence of facts warranting certain actions, such as the issuance of a warrant.

Nolo Contendere

A legal plea whereby a defendant in a criminal case does not admit guilt but also does not dispute the charges, allowing for a conviction without an admission of guilt.