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

question 387

Essay

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

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Definitions:

Res Ipsa Loquitur

A doctrine in tort law that infers negligence from the very nature of an accident or injury, in the absence of direct evidence on how any defendant behaved.

Causation

The relationship between cause and effect, where one event (the cause) directly leads to the occurrence of another event (the effect).

Duty of Care

A legal obligation imposed on individuals or organizations to adhere to a standard of reasonable care while performing acts that could foreseeably harm others.

Battery

A civil wrong that occurs when one person intentionally and voluntarily brings about a nonconsented harmful or offensive contact with a person or something closely associated with him or her. Battery requires an actual contact.