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:

RLC Parallel Circuit

A circuit configuration that includes a resistor (R), inductor (L), and capacitor (C) each connected between the same two points, providing multiple paths for current flow.

Applied Voltage

The voltage that is externally applied to an electrical component or circuit.

Total Current

The combined current that flows in an electrical circuit, which, in parallel circuits, is the sum of the individual currents through each component.

RLC Parallel Circuit

A circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel.