Chapter 4
Series and Limits

 4.1 Finite and Infinite Series
  4.1.1 Finite Series of Natural Numbers (Gauß)
  4.1.2 Finite Geometric Progression
  4.1.3 Binomial
  4.1.4 Infinite Series
 4.2 Taylor–Series
  4.2.1 The Exponential Function
  4.2.2 Power Series for \mathop{sin}\nolimits (x) and \mathop{cos}\nolimits (x)
  4.2.3 General Case
  4.2.4 Example: The Exponential Function \mathop{exp}\nolimits (x)
 4.3 Taylor–Expansion of Functions
  4.3.1 Convergence: Expansion of f(x) =\mathop{ ln}\nolimits (1 + x)
  4.3.2 Alternative way to generate a Taylor Series
  4.3.3 Taylor expansion of f(x) around an arbitrary x = a
 4.4 Further Examples for Series and Limits
  4.4.1 Newtonian Limit of Relativistic Energy
  4.4.2 Limits