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 278

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.
- $$1.06 ^ { 3 }$$

• A) 0.837
• B) 1.191
• C) 0.840
• D) 1.194

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Definitions:

Cellular Slime Molds

Organisms that exist as individual amoeboid cells but can aggregate to form multicellular reproductive structures under certain conditions.

Representative Clade

A group of organisms that together represent a branch of the tree of life, sharing a common ancestor.

Supergroup

In biology, a high-level taxonomic rank above the group level, often used in the classification of life forms that share common evolutionary traits.

Green Algae

Photosynthetic, aquatic organisms in the Chlorophyta division, considered the ancestors of land plants.