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

question 57

Essay

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

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Definitions:

Administrative Expense

Costs associated with the general administration of a business, such as salaries of executive officers, legal fees, and office supplies.

Investing Activities

Activities related to buying and selling long-term assets and various investments, which appear in a firm's statement of cash flows.

Comparative Balance Sheet

A financial statement that presents the financial position of a company at two or more different points in time, allowing for trend analysis.

Financing Activities

Transactions related to raising funds or repaying investors, such as issuing debt or equity, or repaying loans.