Use Mathematical Induction to Prove the Following $$\sum _ { i = 1 } ^ { n } ( 5 i + 8 ) = \frac { n ( 5 n + 21 ) } { 2 }$$

question 87

Essay

Use mathematical induction to prove the following.
- $$\sum _ { i = 1 } ^ { n } ( 5 i + 8 ) = \frac { n ( 5 n + 21 ) } { 2 }$$

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Definitions:

Equilibrium

A situation in a market where the quantity demanded equals the quantity supplied, leading to a stable price.

Surplus

The excess of a good or service that occurs when the quantity supplied exceeds the quantity demanded; surpluses occur when the price is above the equilibrium price.

Price Elasticity of Demand

A measure of how much the quantity demanded of a good responds to a change in the price of that good, indicative of the product's sensitivity to price changes.

Availability of Substitutes

The presence of alternative goods or services that consumers can switch to when prices rise or quality decreases, affecting market demand and competition.