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1.2 Sequences and Series
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Math 101 Chapter 1: Sequences and Series
Gordon Blower
1.2 Sequences and Series
1.3 Sets and numbers
1.4 Archimedes’ Axiom
1.5 Intervals
1.6 Polynomials
1.7 Polynomials and their degrees
1.8 Remainder theorem
1.9 Factorizing by guesswork
1.10 Division algorithm
1.11 Polynomial long division
1.12 Rational functions
1.13 Examples of rational arithmetic
1.14 Induction
1.15 Principle of induction
1.16 Triangular numbers
1.17 Induction step
1.18 Remarks on induction proofs
1.19 The sum of squares
1.20 Induction statements other than identities
1.21 Nonsense by induction
1.22 Pascal’s triangle
1.23 Binomial Theorem
1.24 Binomial by induction: basis
1.25 Binomial by induction: induction step
1.26 Formulas for the binomial coefficients
1.27 Sequences
1.28 Building sequences
1.29 Convergence of sequences
1.30 Examples of convergent and divergent sequences
1.31 Geometric sequences
1.32 Proof
1.33 Series
1.34 Infinite Series
1.35 Partial sums
1.36 Convergence of series
1.37 A collapsing series
1.38 Geometric series
1.39 Proof
1.40 Recurring decimals as geometric series
1.41 Divergent series