It Can Be Shown That $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$

question 159

Multiple Choice

It can be shown that $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$ is true for any real number $n$ (not just positive integer values) and any real number $x$ , where $| x | < 1$ . Use this series to approximate the given number to the nearest thousandth.
- $$( 1.03 ) ^ { - 5 }$$

• A) 0.863
• B) 1.159
• C) 1.154
• D) 0.867

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Definitions:

Appropriation

The allocation or setting aside of funds by a company for a specific purpose or the restriction of retained earnings distributed to shareholders.

Inventory Finance

A line of credit or loan specifically intended to help businesses purchase inventory, often secured by the inventory itself.

Long-Term Note

A debt obligation with a repayment period typically exceeding one year, often used for significant purchases or investment.

Refinancing

The process of replacing an existing loan with a new loan, typically to secure better interest rates or loan terms.