Use Mathematical Induction to Prove the Following for Every Positive $n$

question 6

Essay

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

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Definitions:

Net Present Value

A financial measure that determines the variance between the current worth of cash coming in and the current worth of cash going out over a specified timeframe.

Vending Machines

Automated machines that sell products such as snacks, beverages, or tickets to consumers after money, a credit card, or a specially designed card is inserted into the machine.

Working Capital

The disparity between an enterprise's existing assets and current debts, demonstrating its short-term financial status and operational performance.

Discount Rate

In discounted cash flow analysis, the interest rate that is used to evaluate the present value of anticipated cash flows.