Use Mathematical Induction to Prove the Following $$1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

question 79

Essay

Use mathematical induction to prove the following.
- $$1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

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Definitions:

Cash Flow Growth Rate

The rate at which a company's cash flow increases or decreases over a specific period.

Required Rate

The minimum rate of return that an investor expects or requires from an investment to make it worthwhile.

Timeframe

The period during which certain actions are supposed to occur or a particular event is planned to take place.

Present Value

The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Present value accounts for the time value of money.