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

question 38

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$\sum _ { i = 1 } ^ { n } \frac { 17 } { i ( i + 1 ) ( i + 2 ) } = \frac { 17 n ( n + 3 ) } { 4 ( n + 1 ) ( n + 2 ) }$

---

Definitions:

Variable Manufacturing Overhead

Costs that vary with production volume, such as utilities and indirect materials.

Machine-Hours

A measure of the time that a machine is operated, used as a way to allocate machine-related costs to products.

Fixed Manufacturing Overhead

Indirect and constant production costs that are not affected by the level of goods or services produced, including factory rent, salaries of supervisory personnel, and utility costs.

Unit Product Cost

The total cost associated with producing one unit of a product, calculated by dividing the total production costs by the number of units produced.