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

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Definitions:

Correlation Coefficients

A measure that indicates the extent to which two variables change together, ranging from -1 to 1, where 1 means perfect positive correlation, and -1 means perfect negative correlation.

Diversification Benefits

The reduction in investment risk that is achievable by holding a variety of different investment instruments that have low correlation with each other.

Characteristic Line

A line generated in a statistical chart that shows the relationship between the returns on a security or portfolio and the returns on the overall market.

Market Index

A statistical measure that tracks the performance of a group of stocks, representing a portion of the overall market.