Use Mathematical Induction to Prove the Given Statement for All $$\text { If } 0 < x < 1 \text {, then } x ^ { n } < x ^ { n - 1 } \text {. }$$

question 33

Short Answer

Use mathematical induction to prove the given statement for all positive integers n and real numbers x
and y.
- $$\text { If } 0 < x < 1 \text {, then } x ^ { n } < x ^ { n - 1 } \text {. }$$

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Definitions:

Clavicle

A lengthy bone acting as a support link between the scapula and the sternum, commonly referred to as the collarbone.

Deltoid Muscle

A large, triangular muscle covering the shoulder joint and used for lifting and rotating the arm.

Anterior Cervical Triangle

An anatomical area of the neck outlined by the mandible, the sternocleidomastoid muscle, and the midline of the neck.

Posterior Cervical Triangle

An anatomical area of the neck bounded by the sternocleidomastoid muscle, the trapezius muscle, and the clavicle, containing several important structures including nerves and lymph nodes.