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

question 11

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$$\sum _ { i = 1 } ^ { n } \frac { 15 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 15 n } { 2 n + 1 }$$

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Definitions:

Partnerships

A legal arrangement where two or more parties collaborate in managing and operating a business.

Life Insurance

A type of insurance that protects people against the financial losses that occur with premature death.

Franchising

A business model that allows individuals to own and operate a branch of a larger company using its brand name, systems, and processes.

Start-Up Cost

Initial expenses required to establish a business, including equipment, permits, and marketing.