 1.2.1: Provethat 1/1 .2+ 1/2.3 + ... + l/n(n + 1) = n/(n + 1) for all n EN.
 1.2.2: Provethat 13+ 23+... + n3 = [4n(n + 1)]2for all n EN.
 1.2.3: Provethat 3 + 11+ . . . + (8n  5) = 4n2  n for all n E N.
 1.2.4: Provethat12+ 32+... + (2n 1)2= (4n3 n)/3 for alln EN.
 1.2.5: Provethat 12 22+ 32+... + (_l)n+1n2 = (_1)n+1n(n+ 1)/2 for alln EN.
 1.2.6: Prove that n3 + 5n is divisible by 6 for all n EN.
 1.2.7: Prove that 52n 1 is divisible by 8 for illn EN.
 1.2.8: Prove that 5n  4n  1 is divisible by 16 for all n EN.
 1.2.9: Prove that n3 + (n + 1)3 + (n + 2)3 is divisible by 9 for all n E N. 1
 1.2.10: Conjecture a fonnula for the sum III .3+ 1/3 .5+ . . . + 1/(2n  1)...
 1.2.11: Conjecture a fonnula for the sum of the first n odd natural numbers...
 1.2.12: Prove the Principle of Mathematical Induction 1.2.3 (second version...
 1.2.13: Prove that n < 2n for all n EN. 1
 1.2.14: Prove that 2n < n! for all n 2: 4, n E N.
 1.2.15: Prove that 2n  3 ::: 2n2 for all n 2: 5, n EN.
 1.2.16: Find all natural numbers n such that n2 < 2n. Prove your assertion.
 1.2.17: Find the largest natural number m such that n3  n is divisible by ...
 1.2.18: Prove that IIv'! + 1/../2 + + 1/..,1n> ..,Infor all n EN. 1
 1.2.19: Let S be a subset of N such that (a) 2k E S for all kEN, and (b) if...
 1.2.20: Let the numbers xn be defined as follows: xl := 1, x2 := 2, and xn+...
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
Get Full SolutionsIntroduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Chapter 1.2: Mathematical Induction includes 20 full stepbystep 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 stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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.

Quadrant
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.

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.
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