Use Mathematical Induction to Prove That for All Integers $n \geq 0$

question 4

Essay

Use mathematical induction to prove that for all integers $n \geq 0$ ,
$$1 + 3 + 3 ^ { 2 } + \cdots + 3 ^ { n } = \frac { 3 ^ { n + 1 } - 1 } { 2 } .$$

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Definitions:

Price Inelastic

This refers to a situation where the quantity demanded or supplied of a good or service changes minimally in response to changes in its price.

Farm Products

Goods that are the result of agricultural activities, including crops, livestock, and the products derived from them.

Total Revenue Test

A method used to assess the impact of price changes on total revenue, analyzing if a product is elastic or inelastic in demand.

Elasticity

A measure of how much the demand or supply of a product changes in response to a change in price.