Use Mathematical Induction to Prove the Following $$\text { If } a \text { is } a \text { constant and } 0 < a < 1 \text {, then } a ^ { n } < a ^ { n - 1 } \text {. }$$

question 9

Essay

Use mathematical induction to prove the following.
- $$\text { If } a \text { is } a \text { constant and } 0 < a < 1 \text {, then } a ^ { n } < a ^ { n - 1 } \text {. }$$

---

Definitions:

Personal/Rental

Pertaining to property that is used for personal purposes at times and rented out at others, often affecting tax implications.

Schedule E

Schedule E is a form used for tax filing that reports supplemental income and loss from rental real estate, royalties, partnerships, S corporations, estates, trusts, and residual interests.

Schedule D

A form used with the U.S. federal income tax return to report capital gains and losses from the sale, exchange, or disposition of capital assets.

Mortgage Interest

The interest charged on a loan used to purchase a residence, which can be deductible for taxpayers who itemize deductions on their income tax returns.