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:

Foreclosed

A legal process by which a lender takes possession of property used as collateral for a loan that has not been repaid according to the terms of the mortgage or deed of trust.

Antitrust Laws

Laws designed to protect trade and commerce from abusive practices such as monopolies, price fixing, and other unfair business practices.

Oligopolistic Structure

A market structure characterized by a small number of large firms dominating the market, often leading to limited competition.

Intent To Monopolize

A legal concept referring to actions or strategies by a company designed to achieve, maintain or extend monopoly power, often scrutinized under antitrust laws.