Use Mathematical Induction to Prove That the Statement Is True $0 < a < 1$

question 171

Essay

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

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Definitions:

Scrap Value

The anticipated market value of an asset at the end of its operational lifetime.

Sum-Of-The-Years-Digits

A depreciation method that results in a more accelerated write-off of the asset, calculated by adding together the digits of the asset's useful life years.

MACRS Tables

The Modified Accelerated Cost Recovery System tables used in the United States for tax purposes to determine the depreciation of assets over time.

Allowable Depreciation

The allowable tax deduction for the reduction in value of a tangible asset over its useful life, as determined by tax regulations.