Use the Principle of Mathematical Induction to Show That the Statement

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. ( $$\left( \text { Hint: } 7 ^ { \mathrm { k } + 1 } - 2 ^ { \mathrm { k } + 1 } = 7 \left( 7 ^ { \mathrm { k } } - 2 ^ { \mathrm { k } } \right) + 5 \cdot 2 ^ { \mathrm { k } } \right)$$