The Binomial Theorem States That for Any Real Numbers a and B

question 6

Essay

The binomial theorem states that for any real numbers a and b, $$( a + b ) ^ { n } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { l } n \\k\end{array} \right) a ^ { n - k } b ^ { k } \quad \text { for any integer } n \geq 0$$
Use this theorem to show that for any integer $$n \geq 0 , \sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } n \\k\end{array} \right) 3 ^ { n - k } 2 ^ { k } = 1$$

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Definitions:

Psychological Pricing Tactics

Pricing strategies that aim to influence a customer's perception of the price to make a product more attractive, such as pricing items just below a round number.

Prestige Pricing

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Split Advertising

A marketing strategy that involves dividing advertising efforts among different media channels or geographic locations to target specific audiences more effectively.

Effectiveness Of Advertising

The measure of how well advertising campaigns achieve their intended objectives, such as increasing brand awareness or boosting sales.