Use the Binomial Theorem to Prove the Following

question 41

Short Answer

Use the binomial theorem to prove the following: $$\left( \begin{array} { c } 100 \\0\end{array} \right) + \left( \begin{array} { c } 100 \\2\end{array} \right) + \left( \begin{array} { c } 100 \\4\end{array} \right) + \left( \begin{array} { c } 100 \\6\end{array} \right) + \cdots + \left( \begin{array} { c } 100 \\98\end{array} \right) + \left( \begin{array} { c } 100 \\100\end{array} \right) = \left( \begin{array} { c } 100 \\1\end{array} \right) + \left( \begin{array} { c } 100 \\3\end{array} \right) + \left( \begin{array} { c } 100 \\5\end{array} \right) + \cdots + \left( \begin{array} { c } 100 \\97\end{array} \right) + \left( \begin{array} { c } 100 \\99\end{array} \right) \text {. }$$

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Definitions:

Sensory Memory

The shortest-term element of memory, which allows individuals to retain impressions of sensory information after the original stimuli have ended.

External World

Everything that exists outside of an individual's mind, including physical and social environments.

Script

Predefined sequences or sets of actions that individuals follow in specific situations or interactions.

Sequence Of Events

An ordered list of events or actions that follow one another, often important in storytelling, planning, and process analysis.