Write the Word or Phrase That Best Completes Each Statement $7 ^ { \mathrm { n } } - 2 ^ { \mathrm { n } }$

question 178

Essay

Write the word or phrase that best completes each statement or answers the question.
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 $7 ^ { \mathrm { n } } - 2 ^ { \mathrm { n } }$ " is true for all natural numbers. (Hint: $7 ^ { \mathrm { k } + 1 } - 2 ^ { \mathrm { k } + 1 } = 7 \left( 7 ^ { \mathrm { k } } - 2 ^ { \mathrm { k } } \right) + 5 \cdot 2 ^ { \mathrm { k } }$ )

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Definitions:

Public Policy

Comprises government actions and procedures intended to solve societal issues and promote the general welfare.

Privity of Contract

A legal doctrine that stipulates that only parties in a contract have the right to sue or be sued on the contract terms.

Right to Privacy

The right of individuals to keep their personal matters and relationships confidential and free from public view or intrusion.

Bank's Sale

A sale conducted by a bank, usually involving assets owned by the bank or foreclosed properties.