Use Mathematical Induction to Prove That the Statement Is True $$\text { If } 0 < a < 1 \text {, then } a ^n < 1 \text {. }$$

question 189

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$\text { If } 0 < a < 1 \text {, then } a ^n < 1 \text {. }$$ (Assume that a is a constant.)

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Definitions:

Debt-Equity Ratio

A marker indicating the relative financing tactics of using debt and equity in company assets.

Return On Assets

A financial ratio indicating the profitability of a firm relative to its total assets, demonstrating how efficient a company is at using its assets to generate earnings.

Return On Equity

A financial performance metric determined by dividing net income by shareholders' equity, showcasing the efficiency of management in utilizing the company's assets to generate profits.

Times Interest Earned Ratio

A financial metric indicating how well a company can meet its interest obligations based on current earnings before interest and taxes.