2 + 4 + 6 + + 2n = n1n + 12
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Table of Contents
R.1
Real Numbers
R.2
Algebra Essentials
R.3
Geometry Essentials
R.4
Polynomials
R.5
Factoring Polynomials
R.6
Synthetic Division
R.7
Rational Expressions
R.8
nth Roots; Rational Exponents
1
Equations and Inequalities
1.1
Linear Equations
1.2
Quadratic Equations
1.3
Complex Numbers; Quadratic Equations in the Complex Number System
1.4
Radical Equations; Equations Quadratic in Form; Factorable Equations
1.5
Solving Inequalities
1.6
Equations and Inequalities Involving Absolute Value
1.7
Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
2
Graphs
2.1
The Distance and Midpoint Formulas
2.2
Graphs of Equations in Two Variables; Intercepts; Symmetry
2.3
Lines
2.4
Circles
2.5
Variation
3
Functions and Their Graphs
3.1
Functions
3.2
The Graph of a Function
3.3
Properties of Functions
3.4
Library of Functions; Piecewise-defined Functions
3.5
Graphing Techniques: Transformations
3.6
Mathematical Models: Building Functions
4
Linear and Quadratic Functions
4.1
Linear Functions and Their Properties
4.2
Linear Models: Building Linear Functions from Data
4.3
Quadratic Functions and Their Properties
4.4
Build Quadratic Models from Verbal Descriptions and from Data
4.5
Inequalities Involving Quadratic Functions
5.1
Polynomial Functions and Models
6
Exponential and Logarithmic Functions
6.1
Composite Functions
6.2
One-to-One Functions; Inverse Functions
6.3
Exponential Functions
6.4
Logarithmic Functions
6.5
Properties of Logarithms
6.6
Logarithmic and Exponential Equations
6.7
Financial Models
6.8
Exponential Growth and Decay Models; Newtons Law; Logistic Growth and Decay Models
6.9
Building Exponential, Logarithmic, and Logistic Models from Data
7
Analytic Geometry
7.2
The Parabola
7.3
The Ellipse
7.4
The Hyperbola
8
Systems of Equations and Inequalities
8.1
Systems of Linear Equations: Substitution and Elimination
8.2
Systems of Linear Equations: Matrices
8.3
Systems of Linear Equations: Determinants
8.4
Matrix Algebra
8.5
Partial Fraction Decomposition
8.6
Systems of Nonlinear Equations
8.7
Systems of Inequalities
9
Sequences; Induction; the Binomial Theorem
9.1
Sequences
9.2
Arithmetic Sequences
9.3
Geometric Sequences; Geometric Series
9.4
Mathematical Induction
9.5
The Binomial Theorem
10
Counting and Probability
10.1
Counting
10.2
Permutations and Combinations
10.3
Probability
Textbook Solutions for College Algebra
Chapter 9.4 Problem 1
Question
2 + 4 + 6 + + 2n = n1n + 12
Solution
The first step in solving 9.4 problem number 1 trying to solve the problem we have to refer to the textbook question: 2 + 4 + 6 + + 2n = n1n + 12
From the textbook chapter Mathematical Induction you will find a few key concepts needed to solve this.
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full solution
full solution
Title
College Algebra 9
Author
Michael Sullivan
ISBN
9780321716811
2 + 4 + 6 + + 2n = n1n + 12
Chapter 9.4 textbook questions
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Chapter 9: Problem 11 College Algebra 9
1 1 # 2 + 1 2 # 3 + 1 3 # 4 + + 1 n1n + 12 = n n + 1
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Chapter 9: Problem 12 College Algebra 9
1 1 # 3 + 1 3 # 5 + 1 5 # 7 + + 1 12n - 1212n + 12 = n 2n + 1
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Chapter 9: Problem 17 College Algebra 9
1 # 2 + 2 # 3 + 3 # 4 + + n1n + 12 = 1 3 n1n + 121n + 22
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Chapter 9: Problem 18 College Algebra 9
1 # 2 + 3 # 4 + 5 # 6 + + 12n - 1212n2 = 1 3 n1n + 1214n - 12
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Chapter 9: Problem 28 College Algebra 9
Show that the statement is a prime number is true for but is not true for n = 41.
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Chapter 9: Problem 29 College Algebra 9
Show that the formula 2 + 4 + 6 + + 2n = n2 + n + 2 obeys Condition II of the Principle of Mathematical Induction.That is, show that if the formula is true for some k it is also true for Then show that the formula is false for (or for any other choice of n).
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Chapter 9: Problem 30 College Algebra 9
Use mathematical induction to prove that if then a + ar + ar2 + + arn-1 = a 1 - rn 1 - r
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Chapter 9: Problem 31 College Algebra 9
Use mathematical induction to prove that a + 1a + d2 + 1a + 2d2 + + 3a + 1n - 12d4 = na + d n1n - 12 2
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Chapter 9: Problem 32 College Algebra 9
Extended Principle of Mathematical Induction The Extended Principle of Mathematical Induction states that if Conditions I and II hold, that is, (I) A statement is true for a natural number j. (II) If the statement is true for some natural number then it is also true for the next natural number then the statement is true for all natural numbers Use the Extended Principle of Mathematical Induction to show that the number of diagonals in a convex polygon of n sides is 1 2 n1n - 32.
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Chapter 9: Problem 33 College Algebra 9
Geometry Use the Extended Principle of Mathematical Induction to show that the sum of the interior angles of a convex polygon of n sides equals 1n - 22 # 180.
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Chapter 9: Problem 34 College Algebra 9
How would you explain the Principle of Mathematical Induction to a friend?
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