Use the Principle of Mathematical Induction to Show That the Statement

question 31

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7n - 2n" is true for all
natural numbers. ( $$\left( \text { Hint: } 7 ^ { \mathrm { k } + 1 } - 2 ^ { \mathrm { k } + 1 } = 7 \left( 7 ^ { \mathrm { k } } - 2 ^ { \mathrm { k } } \right) + 5 \cdot 2 ^ { \mathrm { k } } \right)$$

---

Definitions:

Transection

Transection is the act of cutting or dividing something transversely, often used in medical or biological contexts to refer to the cutting of tissue or anatomical structures.

Quadriplegic

A condition characterized by paralysis affecting all four limbs, typically resulting from injury to the spine at a high level.

Nociceptive Pain

Pain that arises from physical damage or inflammation to the body's tissues, often perceived as sharp, aching, or throbbing.

Aching

A continuous or prolonged dull pain in a part of the body.