Use Summation Notation to Write the Given Series in Compact $$\frac { 1 } { 4 } - \frac { 2 } { 16 } + \frac { 3 } { 64 } - \frac { 4 } { 256 } + \cdots$$

question 2

Multiple Choice

Use summation notation to write the given series in compact form. $$\frac { 1 } { 4 } - \frac { 2 } { 16 } + \frac { 3 } { 64 } - \frac { 4 } { 256 } + \cdots$$

• A) \(\sum _ { n = 1 } ^ { \infty } n ( - 1 ) ^ { n - 1 } \left( \frac { 1 } { 4 } \right) ^ { n }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { - n } { 4 ^ { n } }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { n } { 4 ^ { n } }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \left( - \frac { n } { 4 } \right) ^ { n }\)

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Definitions:

Inflation-adjusted Amount

A monetary value converted to reflect changes in purchasing power due to inflation, ensuring comparison over time is more accurate.

Registration Statement

A set of documents, including financial statements and a prospectus, filed with a securities regulatory body to register new securities for public sale.

CFO

Chief Financial Officer, an executive responsible for managing the financial actions of a company.

Regulation A

An exemption under the Securities Act allowing smaller companies to offer and sell up to $50 million of securities in a 12-month period, subject to less stringent reporting requirements.