Use the Binomial Theorem to Prove the Following

question 91

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:

Diabetes

A metabolic disease characterized by high blood sugar levels over a prolonged period.

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A chronic autoimmune disease affecting the central nervous system, characterized by damage to the myelin sheath that covers nerve fibers, leading to various neurological symptoms.

Diabetes

A chronic condition characterized by high levels of sugar in the blood, due to the body's inability to produce or properly use insulin.