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:

Interdependent Self-Construal

A concept of oneself that is closely linked with and defined by relationships with others, emphasizing connectedness and social context.

Interpersonal Self

The aspect of an individual's self-concept that is formed in relation to their social environments and interactions with others.

Public Self

An aspect of an individual's self-concept that is concerned with how they are seen by others and is shaped by social interactions and public roles.

Interdependent Self-Construal

An understanding of oneself in relation to others and a tendency to define oneself in terms of relationships with others.