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:

Dizygotic Twins

Twins born from two separate eggs fertilized by two different sperm, also known as fraternal twins.

Physical Trait

Observable characteristics of the body, including appearance, strength, and genetic features.

Genes

Units of heredity made up of DNA that carry information for the development, functioning, and reproduction of organisms.

Meiosis

A type of cell division that reduces the chromosome number by half, resulting in four haploid cells, each genetically distinct from the parent cell, involved in sexual reproduction.