Find a Formula for the Nth Partial Sum of the Series

question 218

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.
- $$5 + 45 + 405 + \ldots + 5 \cdot 9 ^ { n - 1 } + \ldots$$

• A) \(\frac { 5 \left( 1 - 9 ^ { n } \right) } { 1 - 9 }\); series diverges
• B) \(\frac { 5 ( 1 - 9 n ) } { 1 - 9 } ; \frac { 5 } { 8 }\)
• C) \(\frac { 5 \left( 1 + 9 ^ { n } \right) } { 1 + 9 } ; \frac { 1 } { 2 }\)
• D) \(\frac { 5 \left( 1 - 9 ^ { n } \right) } { 9 - 1 }\); series diverges

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Definitions:

Cumulative Voting

A voting system that allows shareholders to concentrate their votes on a single candidate for the board of directors.

Board of Directors

A group of individuals elected by shareholders to oversee the management and make major decisions for a company.

Preferred Stock

A class of ownership in a corporation with a fixed dividend that must be paid out before dividends to common stockholders and which typically does not have voting rights.

Ownership Interest

Refers to the rights and stake a person holds in a particular asset or business, often entailing voting rights and a share in the profits.