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# Solutions for Chapter 1.2: Mathematical Induction

## Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 1.2: Mathematical Induction

Solutions for Chapter 1.2
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##### ISBN: 9780471321484

Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Chapter 1.2: Mathematical Induction includes 20 full step-by-step solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Since 20 problems in chapter 1.2: Mathematical Induction have been answered, more than 2645 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Dependent event

An event whose probability depends on another event already occurring

• equation of a hyperbola

(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1

• Expanded form of a series

A series written explicitly as a sum of terms (not in summation notation).

• Graph of an inequality in x and y

The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

• kth term of a sequence

The kth expression in the sequence

• Linear inequality in two variables x and y

An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

• Linear inequality in x

An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

• Local maximum

A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

• Logarithmic regression

See Natural logarithmic regression

• Natural exponential function

The function ƒ1x2 = ex.

• Parametric curve

The graph of parametric equations.

• Pie chart

See Circle graph.

• Polynomial function

A function in which ƒ(x)is a polynomial in x, p. 158.

Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

• Real zeros

Zeros of a function that are real numbers.

• Scalar

A real number.

• Sequence of partial sums

The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

• Statistic

A number that measures a quantitative variable for a sample from a population.

• Vertex of a cone

See Right circular cone.

• x-coordinate

The directed distance from the y-axis yz-plane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

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