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7.6: Inductive Proofs

Difficulty Level: At Grade Created by: CK-12
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Vocabulary

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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Difficulty Level:
At Grade
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Date Created:
Nov 01, 2012
Last Modified:
Mar 23, 2016

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