Use the Principle of Mathematical Induction to Show That the Statement

question 75

Short Answer

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-Show that the formula $$2 + 4 + 6 + 8 + \cdots + 2 n = n ^ { 2 } + n + 3$$ obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for some natural
number k, it is also true for the next natural number k + 1. Then show that the formula is false for n = 1.

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Definitions:

Producer Surplus

The difference between the amount producers are willing and able to supply goods for versus the amount they actually receive due to market prices.

Total Surplus

The sum of consumer surplus and producer surplus, representing the total net gain to society from the production and consumption of goods and services.

Tariff Revenue

Income that a government collects from imposing duties on imported goods.

Consumer Surplus

The divergence between the amount consumers are willing to pay for a product or service and the amount they actually pay.