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:

Generation X

The demographic cohort following the Baby Boomers, typically defined as being born from the mid-1960s to early 1980s.

Generational Cohort

A group of people of the same generation—typically have similar purchase behaviors because they have shared experiences and are in the same stage of life.

Demographic Data

Information collected about populations or specific groups, including statistics on age, gender, income, race, and education, used for analysis and policy-making.

Cultural Expectations

These are the shared beliefs, norms, and values that shape consumer behaviors and preferences within a particular society or community.