Use the Binomial Theorem to Prove the Following

question 57

Short Answer

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

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Definitions:

Court

A tribunal, often a governmental institution, with the authority to adjudicate legal disputes between parties and carry out the administration of justice.

Relevant Evidence

Information presented in court that directly relates to the facts in dispute and can help prove or disprove a point.

Direct Evidence

Evidence that directly proves a fact, without the need for inference or presumption, and which in its own right conclusively establishes the fact in question.

Truth

The quality or state of being in accord with fact or reality, often pursued in various disciplines like philosophy, science, and law.