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# 7.6: Inductive Proofs

Difficulty Level: At Grade Created by: CK-12

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### Vocabulary Language: English

arithmetic series

An arithmetic series is the sum of an arithmetic sequence, a sequence with a common difference between each two consecutive terms.

Base Case

In an induction proof, the base case is the anchor step. It is the first domino to fall, creating a cascade and thus proving the statement true for every number greater than the base case.

induction

Induction is a method of mathematical proof typically used to establish that a given statement is true for all positive integers.

inductive hypothesis

In an induction proof, the inductive hypothesis is the step where you assume the statement is true for $k$.

inductive step

In an induction proof, the inductive step is the proof. It is when you show the statement is true for $k+1$ using only the inductive hypothesis and algebra.

Mathematical induction

Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all positive integers.

nth term

The nth term in a series commonly refers to the last term in a series, often left unspecified.

proof

A proof is a series of true statements leading to the acceptance of truth of a more complex statement.

series sum

The series sum is the total sum of all of the numbers in a series.

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Date Created:
Nov 01, 2012