Use the Binomial Theorem to Prove the Following

question 121

Short Answer

Use the binomial theorem to prove the following: $$3 ^ { 100 } = \left( \begin{array} { c } 100 \\0\end{array} \right) + \left( \begin{array} { c } 100 \\1\end{array} \right) \cdot 2 + \left( \begin{array} { c } 100 \\2\end{array} \right) \cdot 2 ^ { 2 } + \left( \begin{array} { c } 100 \\3\end{array} \right) \cdot 2 ^ { 3 } + \cdots + \left( \begin{array} { c } 100 \\99\end{array} \right) \cdot 2 ^ { 99 } + \left( \begin{array} { c } 100 \\100\end{array} \right) \cdot 2 ^ { 100 }$$

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Definitions:

Democratic Popular Pressure

The force or influence applied by the general populace or societal groups to effect change or influence decision-making in a democratic system.

Expressed Powers

Specific powers granted to the government or its branches explicitly mentioned in the Constitution.

Bill of Rights

The first ten amendments to the United States Constitution, guaranteeing certain rights and freedoms to American citizens.

Excessive Democracy

A theory that suggests too much direct participation or decision-making power in the hands of the public can lead to instability in governance.