3.8. Infinite Products 112

Solutions

Chapter 1. Real Numbers

1.1. Supremum and Infimum of Sets of Real Numbers.

Continued Fractions 125

1.2. Some Elementary Inequalities 136

Chapter 2. Sequences of Real Numbers

2.1. Monotonic Sequences 151

2.2. Limits. Properties of Convergent Sequences 162

2.3. The Toeplitz Transformation, the Stolz Theorem and

their Applications 181

2.4. Limit Points. Limit Superior and Limit Inferior 189

2.5. Miscellaneous Problems 208

Chapter 3. Series of Real Numbers

3.1. Summation of Series 245

3.2. Series of Nonnegative Terms 269

3.3. The Integral Test 302

3.4. Series of Positive and Negative Terms - Convergence,

Absolute Convergence. Theorem of Leibniz 309

3.5. The Dirichlet and Abel Tests 324

3.6. Cauchy Product of Infinite Series 333